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32X
1
2
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1
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5
6
GRAFTON'S
GRADED ARITHMETIC
BOOK IIL
BY
E. W. ARTHY,
SUTEBINTENDENT OF CITY SCHOOLS,
MONTREAL.
Authorized for use in the Promnce of Quebec.
FRIOE, 15 OEITTS-
MONTREAL:
F. E. GRAFTON & SONS, PUBLISHERS.
1899,
\
Entered according to Act of ParUament of Canada in fl,,
one thousand eight hundred and ninety-d. bv F TZl' IV"
in f Iio nffl r i.1 , . . "luety six, by H.h. GrAJTON & SoNS.
m the Office of the Minister of Agriculture. ^
I
^
\
5^
.'
NOTE TO TEACHERS.
This collection of exercises has been arranged and
compiled for the use of young pupils. It is intended to
furnish a sufficient number of easy and easily graded
examples. It has been prepared for inductive teaching.
New work is introduced by easy sight examples, the
object being to lead to an almost unaided perception of
processes and principles. Too often young pupils have to
grapple with numerical difficulties when attempting to
grasp a new principle.
Many of the problems are new; others have been
collected at various times during the past twenty years
from sources too numerous to sj^ecify. The merit of the
work (if it has any) does not consist in the originality of
its matter, but in its arrangement and grading.
Nothing is so discouraging to teachers of arithmetic as
the ease with which pupils forget. For this reason,
though the ordinary arrangement by topics has been
adopted as best calculated in the first instance to impress
upon the mind a new principle and rule, one-third of the
book is taken up with review and test examples, and with
exercises intended to secure rapidity and accuracy in the
simple rules and other computations. These exercises
should be taken as occasion demands.
The author desires to express his indebtedness to Mr.
Nevil Norton Evans, M.A.Sc, Lecturer in Chemistry,
McGill College, for revising the section on the Metric
System.
A Teachers* Manual, giving full directions in using
this book, as well as Answers to examples, may be
procured from the Publishers. Price, 35 cents.
ii
'"A
CONTENTS.
Common FRAcrrroNs . . • .
Denominatk Fractions
Practice ....
Cancellation ...
Proportion ....
Metric System ....
Mensuration .
• . 24
Circular Measure .... qq
Percentage
,, ^ 36
Profit and Loss
Simple Interest
Discount
.66
Present Worth
_ •••••... 69
Compound Interest
-o A •••••... 60
JttAPiD Arithmetic
Miscellaneous Examples (\Vi:i'"ti:n-) h/»
Test Exercises (Mental)
' • * 79
Test Papers (Written) .
Review Exercises (Theory) «„
' • • • • . .93
X.
Work by shortest method : —
1. i +
2. i +
3. i +
4. i +
6. i + f--fi; 17.
I
Q
at'
13.
14.
15.
16.
6.
7.
8.
O.
10.
11.
12.
i +
i +
1 +
i +
18.
*",
19.
20.
1
!¥•
1
1
J.-- ^21.
T* - ' 1:' 22.
1
IT';
1
;, J/ 23.
;; 24.
+
+
+
i +
i +
i -
1 __
"6"
i-
rV.
h.
TIT- ,^
1 ^**
1 w X
XT' • _ll
1 . i"
25. J
26. J
27. I
28. ^
20. J
30. I
31. i
32. i
33. ^
34. tV
35. ^ -
36. tV
1
-i-
1
7*
f
^
1 '* .. J
XT'
_ 1
XF- ^
_ 1
XX'
J'i^
B (%7ijf;.
1. i +
2. J +
3. J +
4. J +
6. f +
6. f +
7. f +
8. § +
0. i +
10.
1 +
11.
12.
!■ ^(? 13.
|..»'' 15.
l^j 16.
i^!i 18.
1.:" 19.
20.
2. 4_ 8
2
5
i- .j'l
+
f +
i + f
4 -L. 5
IT T- T-
f -i-
f - I
i-i-
i-i-
■u
21. i
22. f
23. ^
24. f
25. f
26. f
27. f
28. -y-
29. I
30. i
_ iJ
-i-
-i-
-i-
_ 5
"8
-J
5
M a
/To
FRACTIONS.
•t-
■
\
2. Sry^ 4- ITJ.-^, ; 12. 35 _ ;'
4
6. 3G
21. .^^ - .2f
22. 9| - 8|.
• f 3 + 281 -0^14. 3G ^ V J.^^^' 'I " 2f.
1. I X 5.-
2. f X 10.
8. A X 5.
4. tV X 2.
fi- A X a
'«ii. f X 7.
^12- iV X 6.
15- f X 16. - V
10. i X 18. - \^
1'7. i X 20. ' !l.^
i X
18.
19' il X
90.
6.
ft — 9 V» 1 O , i - _ o * *='. 4 J A 0.
" X 11. 14. f X 21. IS 21. , ^ ^2_
1. A
2. T%
8- tV
3.
6.
- xg^ - 9.
4. e -^ 3.
6. li -r 7.
" ^' -2.
3.^
11. If ~5.
12. If -f- 7.-
^ 13. 8J -f 5.
^, 14. 8J ^ 10.
7 JLl •
,± J.
8. f -f 8.
0 i -r 2.
10. f -r 5.
16. 2jV ^ 9. .
(, 16. 2rV.^4.
)-^ 1'7. oj -f 7.
18. l^V -r 10.
^ 4.
8.-^
3
^ V 19. 3j?j.
i 20. 3i
■ \*
IT
21. T*r ^ 9.
22. I- -f 2.
23. f -f. 4.
24. § -:. 6.
25. f ^ 6.
26. f ^ 9.
27. 6,1 4- 4.
.28. 3| ^ 7.
29. 6| 4- 5.
SO. 2^- ^ 3.
^^^
V
'S
1
«ft
F
n.
1. 8} X 3.'^
-.11
16 X
i
21.
101 X 2J.
, a. 7i X 9^
12
18 X
f
22.
305 X 3i.
8. 6§ X 8.
13
20 X
*.
23.
201 X ^.
4. 9i X 7.
14
17 X
f.
24.
224 X \\.
5. 6i X 6.
16
89 X
\'
25.
340 X 8^
6. 4| X 5.
16.
78 X
«.
26.
100 X 9f
'i 7. ^ X 8.
17
83 X
I'
27.
32 X 11§.
8. 8J X 6.
18
51 X
f
28.
40 X 16J.
9. 6^ X 5.
19
. 63 X
f
29.
36 X Ln.
XO. 5J X 4.
20
42 X
G
f
30.
20 X V^\.
1. 19i -
r 3.
8.
22J 4-
5.
15.
230^- -r a
2. 16| ^
- 4
9.
65J -f
9.
16.
321i -r 8.
8. 16§ ^
- 7.
10.
57f -r
2.
17.
101 f -r 9.
4. 12t ^
- 5.
11.
315i -^
- 2.
18.
2161 ~ 7.
6. 24f H
- 8.
12.
213^ -
- 3.
19.
321f -f 8.
6. 191- ^
r 6.
13.
321i -
r 3.
20.
514f -r 5.
7. Vl% -i
r 9.
14.
622i -
r 5.
21„
213*- -r 5.
II.
A oomplex fraotion has a fraction in either its
numerator or denominator, or in both.
Keduce to simple fractions : —
1. 3J 2. 4i 3. 12 4. 15 6. f 6. 3
7 34 IJ 34- "6 T
^
/
w
■ ■ ■ I
COMPLF^^X FRACTIONS.
7 »
8. 6
9- I
10. «
i^
11. -«-
12. 9j
1^
//-
^2. ^.nd the quotient of the 8th divided by the 9th
23- |_X_,\
f
24.
1 K
6 -^ H
27. 8 X 9|
ae. I of 2j 30. . „f .^
ITT
TVof5i
32.
33. 23
21X21
35. 31- j-j^i
fioflf
33. I3|^12f
39. 7f-^3f
25. f of 13|
28. U\x3?jI,
81- f of 1^
14
1^
34. 12f on^
37. ^0^
.40. 3|o<J^
^-8 — i^i
\
DENOMINATE FRACTIONS.
'g-
11. iisiUi
12. iisH
13. |is-i-?
14. f isi?.--'
15. f isf?.,'
.'•'.■ y
III.
^ A {Sight).
"What part (or fraction) of : —
1. 3 is 1? 6. Sis 15?
2. 3 is 2 ? 7. 15 is 8 ?
3. 7 is 3 ? 8. 8 is 1 ?
4. 9 is 2 ? 9. 7 is f ?
5. 12 is 4? 10. I is 4?
16. What part of 30 cents is 6 cents ? ^
17. What part of 21 yds. is 7 yds. ?
18. $12 is what part of $30 ? Of $96 ?
19. What part of a foot is 4 inch^ ? 3 J inches ?
20. What part of an hour is 15 min. ? 40 min. ?
21. What part of a year is 4 months ? 50 days ?
22. What fraction of a yard is 1 ft. 6 in. ? 2 ft. 6 in. ?
23. Express as the fraction of a century 50 years; 70
years ; 20 years ; 5 years ; 4 years ; 2 years.
24. What fractional part of a lb. is f of an ounce ?
25. What fractional part of 3 wks. 2 dys. is 6 dys. ?
15 days ?^. 1 wk. 5 dys. ? ^ 2 wks. 4 dys. ? j ; '
26. Express f of a dozen as a fraction of ^ of a score. 2
1. Express 3 pints as a fraction of 12 gallons. y_6:
2. Express 3 dys. 16 hrs. as a fraction of 5 weeks. -
3. Express 40 seconds as a fraction of 3 hrs. 24 min.
4. What fractional part of £1. is 16s. 8d. ?
6. Wiiat fractional part of 5 yds. is 7| inches ?
6. What part of a ream is 7 quires 20 sheets ?
7. Ileduce 3 gai. 1 qt. to the jracllou of 3G gaiious.
OA-X^v^
I
6
(« I
V.
DENOMINATE FKACTIONs.
8. What part of $58 is | of $69 1
e. Eeduce J of 28. 6d. to the fraction of J of £9 «.
10. 1 educe A of a mile to the fraction of 220 ti
n. £.xpres3 1| as a fraction of 2i " ^''^^
12. Express ^ of a mile as a fraction of i of a mil«
14 E™ t :; ^r n ^ ^'■^^'^™ "^ *" ^° "
P^ess ,^ ot £1. as a fraction of Is
le E™ !":;"--;- ^-tio„ of a sq. rod.
21. What fraction of 1 TuAT- o /T ' ^''- '
22. Value of 2 yds. 2 ft 3 in ^'''- ^ ^'- ^ ^'^
C (Questions 1-lS at sight).
What decimal fraction of :_
1. 2 is 1 ?i' s o • ^,
1 fi fa K 9 / , ^ . . "^ 3 » J'
2. 8is2?.3i' e. 15is5?.j
J^4. 16is6?.3iv8. 20is2 ,| la" 7/ /^ «
^13. What decimal of a century is l^*' '^ ' ^'^^^ ^
years^?^ 33J years ? 8^ year^ ^ ^^ ^'"^ ^ «3
14
V,,n ' ° J years?
day. "'^'- -^^ "^w. 30 sec. to the decimal of a
17. Eeduce 8 cwt. 34 lbs, to the decimal o' a ton
.': s=i":r:::Lrr:r;£■~
.X
DENOMINATE FRACTIONS.
21. Reduce 2| miles to the decimal of 22 miles.
22. Eediice 1 qt. 1 pt. to the decimal of 1 bu. 1 pk.
Igal.
23. Reduce 1 ac. 1-il sq. rods to the decimal of 5 ac.
50 sq. rods. ^
IV.
Find the value of
1.
2.
3.
6.
^6
9.
10.
11.
Z^12.
13.
^-14.
15.
16.
17.
18.
10.
20.
^21.
^^22.
TTT
of a foot,
^x of a yard,
of an
or an acre. .
of 5 dys. 14 hrs. 38 min. n^y^jJiMM ^ ' ^ "^ ' ^^'
of £5
24
9
TTT
1 9
11.
1 2
If of 17 cubic feet.
4-3665 weeks.
12-4235 acres.
590-357 pecks, -j ^( ^ Y'
2-725 miles. ,
•4375 of a shilling. ^ .
1-085 of 36 gallons.
•09375 of an acre.
•02755 of 5 days, i -/
c? ^'^^ /• 7
/
/ ...• / ~.-
/
/^ ^/' ^ &€i-<I-
•625 of 3 yds. 2 ft. 6 in.
4-045 of 1 cwt. 82 lbs.
3-125 of 10 yds. 2 ft.
'695 of If miles.
i of £3. 9s. 2d. - -65 of £2. 8s. 4d.
•705 ton + 3-375 cwt. + 2-8 lbs.
i gal. + i qt. + 1| pts.
f week + I day + If hours.
3-42 mi. — 1256 rods — 12'5 rods.
I
> .A.A_ Q^i
i I
■Uix^Pip^iV^ractice the v|lue of :-f "" '
I. 508 articles at 50 f.
-i
:;^'^-^
:5'
4^
1 f
/
■^
2. 305
3. 576
4. 704
6. 198
6. 648
7. 211
«
((
f<
ti
«
«
at 25;^. o. 440
at $1.33^. 10. 506
at $3.20. 11.409
at$416f. 12. 316
at$1.12|. 13. 127
at $2.10. 14. 209
8. S6(i ari&l^s^^ ^^^^.^\
«
te
te
tt
it
at $1.06|
at $2.37J,
at $3.75.
at $4.40.
at $1.87i.
at $10.05.
16. 17 chests of tea. each 59 lbs., at SSJ/ a lb ^r
10. 158 tons of coal at «f^ ^qi 4. ";
17. 170 lbs. soap at 8^^ a lb. / <v^/^ 1 -^
19 f 9rn ^'' ^ ""' ^'''''' ^' '^^i^ ^'ib. % .
19. 1260 pineapples at 161/ each. ^;,. -^
20. 503 acres of land at 87^/ a sq. rod. U. ^ ^ , i.
^1= ^^^ acres of land at $1..'^7; a so rnri ^ w / ^
26. 5 mJes 550 yds. of railway at $1600 the m t.
26. 25 days 7 hours work'at $2.40 a day (10 hrs)
27. 7 pecks 5 quarts of cherries at SO.Io a peck.
28. II tons 760 lbs. of coal at $6 a ton. ^
.4o 70 ^ • ^/onn "'• ■ ' ^"'-^ "™ ^' »l-50 a yard.
. Il ■ 20 cT f ? :'»• ^"^^^ °^ ''^■^•^ ^' »55 an a'^re
i ::■ ::" I""'- °* "''■'^p '™" ^t $15 a ton.
CI!' .0 iT"!^ " ^''f '^ °f P-Per at $2.40 a ream.
. ^^- "3 "^«- 11 oz- of tea at $0.80 a lb
aa \ ^"""^ f,iT'''' "^ '""^'^ ^' »9 *e yard.
36. 1 mile 1100 yards of barbed wire at $30 the mile.
-»>.
\
"i.^
'^' f-iOchX 1
^>i.^.Vl..u,Vy'i;^.; J
^•Hf'.'XKO I X^^ 1
87.
>vvj'^.0'i..^,,^ 1
88.
1^ ba^^l
89.
%0.
$1.06i 1
41.
$2.37J, 1
42.
$3.75.
43.
$4.40.
44.
$1.87i.
45.
46.
M^48.
$10.05. '
1
49.
1
60.
CANCETXATION.
5 yds. 1 ft. 9 in. at $1.G2 per yard.
17 acres 2057 sq. yds. of land at $18.72 the acre.
18 yrs. 5 mos. 1 wk. salary at $1000 per year.
Salary for a year at £1. Is. ll|d. per day.
Rent of 29 houses at £13. 14s. 2d. each.
1309 roubles at 2s. 6Jd. each.
706,500 fire bricks at £3. 13s. 6d. per thousand.
90| dozen pairs of boots at 12s. 9d. a pair.
107 shares at £93. 15s. 8d. each. ., /.
27 yds. 1 ft. 5 in. at $0.45 per yardT
15 acres 2662 sq. yds. at $1.10 per acre.
154 bu. 3 pks. at $1.00f the bushel.
24 yrs. 5 mos. 3 weeks at $150 per annum. ,/
25 tons 155 lbs. at $16.80 the ton. j^u-.^^.
VI.
Find the value by cancelling of : —
1. 3 X 15 X 4 2. 7 X 25 X 16 3. 8 x 14 x 24
20 X 12 X 9
8 X 30 X 14
32 X 12 X 7
4. 28 X 5 X 12 5. 2x5x7 6. 5 x 21 x 32
20 X 7 X 32 10 X 11 X 11 48~x 35 x 3
7. 2 X 50 X 11 8. 56 X 42 X 9 9. 30 x 6 x 16
33 X 4 X 10
7 X 8 X 27
3 X 8 X 40
10. 17 X 85 X 4 11. 5 X 81 X 77 12. 90 x 40 x 42
20 X 3 X 3
11 X 55 X 63 100 X 63 X 24
\
I
■i)
13.5-5 X •081x4-9 14.2-1 x-.^-c.; 12-6 15.4-2 x 14-3 x '66
CO v^ /j.O -- -oo
uu ^
4-2
A OO
Ox
x=5G
Art O
r\ -4 A -4 <--\ -«
oU XUJ4X i'ili
/'>
2-S
^: On -^
•J
S-'o
«) c -
10
PROPORTION.
VII.
PROPORTION.
1. If 12 yds. of cloth cost $15 wliafc w,']] q ^
2. If 57 cwt. of surrar cost toia f ! H ^ ^^'- ^^^^ ?
3 Jf tlm , 1 ^^^' ^^^^ will 95 cwt cost ?
<*. It the yearly rent of a farm of 1«9 a ^ i^ !
what is the rent of a mrt of .> . ^''''^^ ^^ ^^^3,
4 T* oor ^ ^* ^^ contamincT 49 aprp« ?
4. If 385 yards of linen cost ^Cv^ I
can be bought for $18 ? ^^^^ ^63, how many yards
Vlf 96 men reap 40 acrp«^ nf r^ - -
■ 2f -n Win reap i ^..Ti:]."! z:z: r'' ''-'
'7. If 84 sheen r.n 1 '''''' P^"^^^"^ ^^ 266 days V^rnj.
for 9-wtf:rirr!.r'™^^"^^-^* «-
■ong wai the p.oviZ: Cf""'"^"' "^ ^O" -- : h w
w^'l'a s^r"'. '"" °' ' ""''' "-■^■^ - «4.75. what
additional n,en „,ust he empLy ? ^^'' ^°^ ""^"^
11. What will 10 hnvpo .f
cost $5i ? ''°'"^' "^ °'^^'g«^ «o«fc, if 3J boxes
walif in" J :* ? """ '' ^ °^ ^" '^-' '^o- fer can I
14. If 3h barrels of apples cost tlA i.
can be bought for $20 ? ' """^ "^^"^ ^^^^^^s
15. i of a race is 500 yards, how long will /, be ?
\
PROPORTION.
11
16. ^ of a city contains 9000 inhabitants; what will
^ of it contain ?
^ 17. If 7| acres be ploughed in GJ hours, how long will
it take to plough 3|- acres ? •
18. In how many hours can a field of 3 J acres be
reaped, if one of 5 J acres is reaped in 6 hours ? ti ' , -, . .
10. If 100 dinners can be paid for with £3 J, how'
many can be paid for with £7^ ? .:!'.;•
^^ 20. If a certain quantity of corn feeds 12 horses for
Hi days, how long will it feed 45 horses ? 3 ' - - ■ .
21. How many men can perform in 1-68 days a piece
of work which 120 men perform in 2-66 days ? ' ' . -
22. If 1^ yards cost 17^ cents, what will 3-^ yaKff^
cost r •
23. If 11 J cwt. cost $5|, what will 4} cwt. cost ? . - ' '>
24. If 3-75 cwt. is carried for ^0-875, what weight
should be carried for $2-625 ? ' :^ ,— °
25. If 2-875 cwt. cost $16-1, how much can be bought
for $19-75? V J) . V'- '
26. What is the rent of 21 acres 140 sq. rods of land
If the rent of 36 acres 120 sq. rods be $42 ^^ :S-
27. If a person walks 17 miles in 5 hours 12 min. 31
sec, how far can he walk in 3 hours 40 min. 36 sec. ?
28. If the earth moves 69,000 miles in its orbit in an
hour, through what space does it move in 16 min. 48 sec. ?
^^ 29. If I lend a person $100 for 12 weeks, how long
ought he in return to lend me $175 ?
30. If f lb. cost $1, what will f of 14 lbs. cost ? a^-:^-;^ /"
31. If a field of IG acres produces 440 bushels of
wheat, how much will be grown on 22 sq. yards ?
32. The shadow of a man whose height is 5 ft. 3 in.
was 4 ft, G in. at the same time that the shadow of a
steeple was 156 ft. Mnd the height of the i
3pl
e.
12
PfiOPOBTlON.
C^ 33. How long would an icebem h^ fl«„*-
breadth bei„g 20 feet ? '^"' "'^''' »''«
' 35. Wiiat will 33i dozen of A,.„ii- •
rate of $49 for 82 do/en a'd 8 itUes' "" '"' ^' ^"^^
^ wo:m /c;;:^f ::;/^^^ >-^^ »^ ''- -e le,., what
37. How many yards of carpet 175 feet wid» w ]^
cover a floors yards long and llfeet broad' ^°""
i-"\iirf::it:.::fr ^^^'^^^^^^^^ ->>-
being 35J feet ? '" '""" ''^«' ">« length
irteoif'' '""^ *=°^' ^'-''^ -'>''' -IJ 31-5625
ttitiscifhor/^^^^-'"^^'^"--'--
rate per hour dnp* if f i .. "^^"""^^s to 8; at what
forstoppaS"? ' ""'""'^^ '^'"S allowed
^ 43 From | of 5 cwt. 28 lbs. take i of 4 cwt 5fi lb« ,
£nd the cost of the ren.ainder at $0M forlcwt 28 il
44. How long will it t^l-„ t„ ° ^^ ^'^^•
long. 12 ft broad Z Oft ''^''' ^ """^^ ^^ ft,
yards 5 ft in it:: 26 ir/"^' ^' "^^ ^^'^ "^ ^ -"^^^
^^fqs^;s3-5-^--.Ht
reri„irtS,Srf:f;oif'---va.neofthe
METlilC SYSTEM.
13
vm.
METRIC SYSTEM.
Metric Weights and Measures are those whose units
increase and decrease regularly by the Decimal Scale.
The metre is the base, and from it the metric system
derives its name.
The metric system has three principal units : the metre
for measurements of length, the litre for capacity, and the
gram for weight.
The ?iigher denominations are formed by prefixing to the
name of the unit the Greek numerals : Deca, signifying
10;^ Heoto, 100; Kilo, 1000; Myria, 10,000.
Tho lower denominations are formed by prefixing to the
name of the unit the Latin numerals: Deci, signifying
iV or -1 ; Oenti, t^tf or -01 ; MiUi, i^jht or -001.
JK^.,)Kilometre = 1000 metres.
/Centimetre = Tff^ of a metre.
Money.
100 centimes = 1 franc (fr.)
Length.
10 millimetres* (mm.) = 1 centimetre (cm.)
"^
10 centimetres
10 decimetres
10 metres
10 decametres
10 hectometres
10 kilometres
1 decimetre (dm.)
1 metre (m.)
1 decametre (Dm.)
1 hectometre (Hm.)
1 kilometre (Km.)
1 myriametre (Mm.)
Only units printed in blacic letter are in common use.
14
if
ill
METRIC SYSTEM.
Si^RFACE Measure.
100 square millimetres = i •au.i* «««♦. ^ f
100 square decunetre.s = 1 «,„^ „.„. ^^^_ \^^
100 ceiitiarcs (ca.) = i ,„ („)
100 ares — i ,. » /tt »
— 1 hectare (Ha.)
A ccnhan is the same in size as a sj. mHn.
mnn ,• •„• Solid Measpke. l—
1000 cu ,.e luillnnetres = 1 cub.c ce„«.™e,™ (ou. em )
1000 cubic decimetres = 1 .„„. m.t« (cu. m )
In measuring wood tlie o«i;c viHrc is called a Stere.
Capacity.
= 1 centilitre (cl.)
= 1 decilitre (dL)
= 1 litre (1.)
= 1 decalitre (Dl.)
= 1 hectoiitre (HL)
Weight.
= 1 centigram (eg.)
= 1 decigrai'i (dg.)
= 1 arram (g.)
= 1 decagram (Dg.)
= I hectogram (Hg.)
= 1 kilo«rram (Kg.)
1000 kilograms make a metrio ton.
Equivalents.
1 metre = 39-37 inches. 1 litre = 176 pints.
1 ki ome re = -6214 mile. 1 hectolitre = 22-01 gaL
8 kilometres = 5 miles (nearly). 1 gram = 15-432 graLs.
1 sq. meti^ = M96 sq. yds. 1 kilo = 2-2046 lbs.
1 hectare = 2-471 acres. l a,etric ton = 1-1023 tons
10 millilitres (ml.)
10 centilitres
10 decilitres
10 litres
10 decalitres
10 miilig^rame (mg.)
10 centigrams
10 decigrams
10 grams
10 decagrams
10 hectograms
*
v
('
METRIC SYSTEM.
A {Length).
Tlie metre is the principal unit, and is usee',, like
yard, for measuring lengths of materials, such as cloth,
for short distances. For long distances, as along roads
railways, the kilometre, like the 7iiile, is used.
1 metre = 39-37 inches.
1 kilometre = 0-6214 mile.
1. How many metres in a decametre?
Hectometre ? Kilometre ? i ^
J" M
2. What part of a metre is a decimetre ? ^
Centimetre ? Millimetre ? 2
3
3. Read in terms of the metre (or kilo- S-
metre) and one other denomination : — 11
17-5 m. 41-625 m. 9-327 Km. 1 m. ?
32-2 ra. 54-886 m. 643 Km. -01 m. §;
64-25 m. 29-7 Km 5-68 Km. -001 m. I
23-62 m. 99-9 Km. 0-563 Km. -001 Km. 2
15
the
and
and
4. Express in terms of a metre : — .
5 m. 3 dm. 24 m. 49 mm. 2-3090 Km
17 m. 24 cm. 64-38 Km. 27-056 Km,
6. Change:—
5747-3 m. to Km.
58-5 m. to cm.
5335 m. to mm.
o
3
9471263 cm. to Km.
4-8735 Km. to m.
372-7575 m. to cm.
6. What is the total length of 5 pieces of
cloth measuring respectively 12-6 m., 9-75 m., 26-08
3-56 m., 31-5 m. ? f-;/-^?^^^"-
7. If the work done by two men measures 18 m.
cue has done 8-75 m., how much has the other done ?
m.,
and
/'^y-
?,>
IG
METIirC 8Y8TEM.
■I
7^
o
* V T -
8. I ow ,m.„y Kn,. i„ 8,r72 m. niulliplieil by 2036?
e. C».,t of ; 7 „,. of silk „t "■50 francs tl,o uLe ? ^ V^' ^'
10. A luerclmnt ina.lo a profit of 1200 fn.ncs ),v
my.ng n ,„oee of cloth at the mte of 7-50 franc, for 5-30
>"•. nnd s.. l,ns it at the rate of 24 francs for 15 n>. How
niiicli did he buy ? t 5 .' . .->fj,
Uo 1 walk in 7 days, going to and fro once a day ? ?. 9 4 /
13 At 7-056 Kin. a,, hour, how far shall I go i„ 6 ''^
hours 24 mm. ? >/ S ' . / S" 5i cy /U>, ,
B (Surface).
J
2
3
^
5
6'
7
fl
.9 10]
20
JO
50
00
1 ■
7/?j
ao
90
0.
—
m
the next l,iri,„r W '"""°' "■ '""=■■ ••''"''■nmation nmko a u„it V
The sjw. metre is used in measuring ordinary surfaces
as floors, ceilings, etc. It is equal to about 10-| sq ft
\
2036 ?
tre? ^^i^' '^
'an OS by
for 5-30
1. How
my Km.
go in 6
length,
unit .1
lacea of
rfaces,
tfc.
cd in
MKTKIU aYSTKM.
17
1. 7Tf
Ldw many sq. nietrus in a sq. Dm. ? A s<i. llm. ?
A S(j[. Km. ?
2. How many contiareH in an tiro ? In a hectare ?
3. What part of a Hiu is m are ? A centiare /
4y JVhafc pjirt of a sq. m. is a sq. dm. ? A sq. cm. ?
6. ][ovv many sq. dm. in 5 sq. m.? 8 sq. m.? 15 sq. m.?
6. Ifow many s([. cm. in 4 s(i. m.? 7 sq. m.? 9 sq. m.?
7. How many sq. m. in 3-45 Ha. ? lO-OO Ha. ?
3. Add 704G3 Ha., 08-45 a., 3-078 Ha., 73-56 a..
2-7608 Ha., 4237 a.
^•'
/.
9. How many sq. m. in a blackboard 2*5 m. long and
1*2 m. wide ?
"^J- ''w-
1
10. How many sq. m. ni the floor of a room 9-75 m.
long and 5-33 i m. wide ? t^ ) -•' i. -
1 1. How many Ha. in a field 220 m. square ? ^f ' 5 ^
1 2. How many sq. m. of surface have the walla of a
hall 14 m. long, 11-5 m. broad and 9-25 m. high I j^^]\^\^^ \
13. How many panes of glass, each 1*25 m. by 1 m.,
would be required for 23 windows, each 5 m. by 4 m. ? g ^ ;, /ia-yuo
14. Into how many fields, each containing 246*53 ares,
could a farm of 41-9101 Ha. be divided ? j 7 > '■
15. Cost of 1-5340 Ha. of land at $2*385 an are ? 3 6 S
16. What is the length of a court whose breadth is
15-5 m. and area 2-945 sq. Dm. ? \^ ry-t-w
17. What is the area of tlie walls, floor and ceiling of
a room which is 11 m. long, 8-25 m. wide and 6-75 m.
high? j.a tX '%)%' -^i vrx^
18. If 21-45 Ha. of land can be rented for-486-75
francs, what will be the rent of 2800 Ha. ? . [ -7 i uU>rX.^
10. Cost of covering the surface of a box 1*2 m. long.
• SVJ'
I
•6 m. wide and -25 m. higli at -006 fr. per sq. cm. ?
)
(/ 0 . ^ {^.
18
!■■
METRIC SY3TE31.
C {Solid Measure),
Cubic metres 1000 (10 x 10 x 10) cubic decimetres.
i^O^'o:^;J^^^ ^^ *^e -its of length, .., 100.
1. In a cu. metre how many cu. dm. ? Cu. cm. ?
2. What part of a cu. metre is a cu. dm.? Acu.cn..
3. Jixpress m terms of a cu. m. 27 cu dm • i «?
V7 ' Lr;- '' ^"^ '-■ ■' '' - - '"^ - -.: ,>
-4. Eead 4-406 cu. m. ; -004017 cu. „,. ; -46 cu m
Q.ocr 1 ^ " "" ^" ** room Wt
8 25 m. loner, 5-64 m. wulo o^rj 9.«r ^. , . , ,
it- Y ^
.)
/
Ve^ci,
\
METRIC SYSTEM.
19
D {Capacity).
s., lOOti
!ie next
?
. cm i
3U. DP
long
svooc
y
'•^.ci.
Litre.
Cubic deoimetre.
The Litre is the principal measure, and holds about a
quart It has exactly the same capacity as a mhic
decimetre.
The Hectolitre is equal to about 22 gal. or 2f bushels.
1. How many litres in a HI. ? A cu. dm. ? A cu. m. ?
2. How many cu. cm. in a litre ? In a HI. ?
8. Eead and express in terms of the litre 6-049 Kl. ;
24-5705 cl. ; 1567-009 Dl. ; 630485 dl.
4. 364 dl. leaked out of a cask containing, 73-0025
HL How much was left ? V p • (- o d 1? ' '^ ' '-"
6. A gentleman buys 1-48 HI. of wine at $0.55 a litre,
72 1. at $0.45 a litre, and 3 HI. at $1.05 a litre. Find the
cost. /^ rj y- \ . ^ (•:
6. Find tho value of 1180 Kl. 6 1. of barley at 20-05
francs a HI. !) , ,\ ' ^^j' / ^
7. Divide 203 1. of soup among 18 men and 22
women, giving each man double a woman's share.
8. How long will 215792 1. last if 674-35 L is con-
sumed weekly ? ^/, OTiyf->^ ;-. / •j'^ / ciX-ATr-K-L
0. A person allows 18*948 cu. m. of water to run
from a tank containing 27,875 cu. dm. How many litres
are left in. the tank ?
»i
20
METIIIC SYSTEM.
10. A wine merchant boufrht fi'?". wi t •
francs DPr Hi i ^"I'o^ic ^m 111. of wme at 60
rancs per HI., and a certain number of HI. of brandy at
1 / 5 francs per HI. He miVI f^q onn 4^ . oranay at
TTr^,„ I, ' P ^ od,900 francs for the wholp
How much brandy did he buy ? *
1 1. How deep is a tank to hold 9000 1. if the bottom
IS a square measuring 1-5 m. on a side ? ^
E {Weight).
• i
Cubic centimetre. Gram.
A cubic centimetre of water weighs
a gram. ^
■fffram is used to weigh gold, sUver
ana drugs.
Akilogmm (called kilo) h used in Kilogran,:
we.g .ng all common articles, as groceries, etc.
A .«» ,s used in weighing coal, hay and heavy articles.
Akilo=2-21bs. A metric ton = l-l tons Av.
1. How many ^ams in a kilo? In a Hg. ?
2. W liat part of a ton is a kilo ? '
3. Weight of 1000 cu. cm. of water? '
4. Weight of a cu. m. of water ?
6. Weiglit of a litre of water ?
-f^rof^^::^^-^^:--*--
7. Change 20-426 kilos to grams; to tona
8. Change to Kg. 553-273 g. ; 48-03 g ; -094 g.
\
METRIC SYSTEM.
21
ine at 60
brandy at
>he whole.
le bottom
tides.
v.
rill be
0. A butcher buys one bullock weighing 382 kilos at
1-35 fr. a kilo, another bullock weighing 341 kilos at 1-25
fr. a kilo, a cow weighing 280 kilos at 095 fr. a kilo, and
a calf weighing 59 kilos at 1-75 fr. a kilo. Find the total
cost.
10. What quantity of tea at 8-75 fr. a kilo ought to
be given in exchange for 700 kilos of sugar at 1-35 fr. a
kilo?
11. At 1-5 cents a kilo, what will 3*25 tons of hay
cost ?
12. At $8 a ton, what will the coal cost to supply a
factory for a week, if 250 kilos are burned each day ?
13. If 7-25 kilos cost 399 francs, find the cost of 43*5
kilos.
14. How many loads of earth, each equal to a cubic
metre, will it take to fill an excavation 4 Dm. long, 8 m.
wide and 2*4 m. deep ?
15. What is the value of a nugget of gold 2-6 cm. long,
2*3 cm wide and 0-65 cm. thick at $15.40 a cu. cm. ?
16. What is the length in metres of a gravel walk
which is 2-4 m. wide and covers an area of 89 1 sq. m. ?
17. What is the height in metres of a wall which is
180 m. long, -625 m. thick and contains 562*5 cu. m. ?
18. Make out the following bill: —
52-25 HI. of wine at 245 francs a litre,
18 HI. of wheat at 18-25 francs per HL,
•1 ton of sugar at 1-05 francs a kilo,
135*5 m. of plank at 1*20 francs a metre.
22-5 steres of wood at 1750 francs a stere.
10. The wheel of a locomotive is 4 J m. in circumfer<
ence; owing to the state of the rails it loses 15 turns in
every 100 revolutions. What distance is gone over in
Ou,i.uv uilriiS ui tiie wTiuel f
22
METRIJ SYSTEM.
Metric System :- "*" ^"'^"^^ ^'^^ ^'^rioua meaaures inThe
Each side of this square
measures
1 decimetre, or
10 centimetres, or
100 milhmetres, or
3*937 inches.
which has the dimensi:
ons
A litre is a cubic measure, each side of
of tliis figure.
A cubio centimetre of pure water at 4" C. weighs a gram.
1 cubic decimetre = i „»,« = iMo^ram
1 cubic centimetre = 1 milliiitre = : gram.
-1-2
-1-4
—1-5
1-6
X^
,^1
WEIGHS
i'lii
—1-8
inches.
.10
1. How many litres iu 6-5 cubio metres ?
of wate!"' ""°" " '"°="^""^ °^ -^^56 cubic metres
\
METRIC SYSTEM.
^
emistry,"
rea in the
sions
rram
3
4
5
— -6
— -8
.10
I tains
tres
3. What is the weight of water required to fill a
cistern 90 centimetres long, 64 centimetres wide and 36
centimetres deep ?
4. A litre of a certain gas weighs 1-675 grams. How
much does a cubic metre weigh ?
6. How many litres in a vessel whose capacity is U
cubic metres ? r j ^
6. How many cubic metres in a rectangular tank 125
cm long, 80 cm. wide and 60 cm. deep ? How many litres?
What weight of water would be required to fill it ?
7. How deep must a cistern be to hold 8000 litres if
the bottom is a square 2-5 metres on a side ?
8 Find the weight of a bar of iron 50 centimetres
long, 4 centimetres wide and 1 centimetre thick if iron
weighs 7-8 times as much as waten
n-i ,1' ,^^^V' ^^^ ""'^^^'^ ^" ^''''"^^ °^ 2J cubic metres of
OU that weighs ^V as much as water ?
10. Find the weight in metric tons of the volume of
water contained in a cistern 4-35 m. long, 3-64 m. wide and
^ as m. deep, supposing the water to be at 4^ Centitrrade
Change from the English to the metric system, o^r from
the metric to the English system, using the equivalents
given on p. 14 :—
1. 35 yds. 2 ft. 9 in. to metres.
2. 3-75 metres to yds. ft. and inches.
3. 3 mi. 130 rods to Km. ^. 18-25 Km. to mi. and rods.
6. 6 lbs. 4 oz. to Kg. 6. 36,000 eg. to oz.
7. 356121 kilograms to cwt. and lbs.
8. 4 sq. ft. 72 sq. in. to sq. m. 9. 45 sq. m. to sq. yds., etc.
1 0. 2 ac. 140 sq. rds. to Ha. 1 1 . 3-5 Ha. to ac. and sq. rds.
12. 3 gal. 2 qts. 1 pt. to litres. 13. 36-7125 HI. to gal.
14. 1800 gallons to cubic metres.
15. 47-S7o cubic decimetres to gal. qts. pts.
24
MExXSURATlON.
;v 1
Pi
IX.
MENSURATION.
-face nlZil'!,2;r' '"" '' "'■ "™^''- Knd its
4. Wl,at will be the cost of fln "'""' ^"' '
^ '7. Cost of carpeting a room 1« ff ^\
^ inches wide at $1,871 perylrZ '^" ""'^^ '"'P^' ^7
8- How many yards of carDef- 97 ' ^.
-cover a iioo. .. ,, 3 ,, ,„„^„ J^^ ^S^.tUt ^^"
'4i«,.s?;iririX^^^^
,/ 10. How many bricks each q : ^' ^"'^ '
^wiu CO tbe z o. atcr .3-^7rh;y;^-'
V"eJetreottratr'^\^:"-f^i-»..
Knd the length of the floor '"'^'' '^ ^^^'^O-
12. How many tiles Pinh o • i.
the floor of a hall 20 ft.' 3 i„ by ntl "^""'' ^'" ''"^^^
ea "fofAr i ;u;i'ri:s^^^^^^ t^ ^. - - ^ --^
the hall. ^' '' ^^^•-^- ^ind the width of .
\\
MENSURATION.
25
-0 ft. by 13 ft. 9 in. Find the cost of staining the border
oi the hall at 27 cents a sq. yard.
^ 1 6 If the length of a rectangular field is 15 rods, what
must be Its breadth so that it may contain exactly an acre ?
^ 16. How many acres of ground are occupied by 100
miles of a road, 63 feet wide ?
17 How many yards of fencing will be required to go
:^ i^und a field 40 rods long, which contains 5 acres ?
^ 18. How many inch cubes can be cut out of a cu yd ?
, . ^o .!^; ^^'""^ '" ^^'^ '''^'^ '^^''^^"^ ^^ "" blo^^ of stone 3 yds.
^ 1/^2 ft. long, 2 yds. 2 ft. broad and 1 yd. 2 ft. thick ?
lA u^-°/ .^r ""^^"^ ^"^^^ ^^- ^^ ^^^^^ will a cistern contain
^which IS 7 ft. 6 in. long, 4 ft. 6 in. broad and 4 ft. deep ?
21. How many gallons of water will the cistern hold if
a gallon contains 231 cubic inches ?
22. The content of a cube whose side is 2 ft. 3 in. ?
23. What will be the weight of a brick wall 10 ft. W
t^'u ?• ^'^^' ^""^ ^^ ^^' ^^^^^' '^ ^^^^' ^^^- foot weighs
IzO lbs. ? °
24. How many cu. yards of earth will be cut out of a
dram 420 ft. long, 2 ft. broad and 4 ft. deep ? In what
time will a man complete the excavation, allowing that
he can lift 500 cu. ft. of earth per day ?
25. A canal is 300 yds. long, its breadth is 5 yds 1 ft
and Its average depth is 5 feet. What weight of water
does It contain, a cubic foot of water weighing 62J lbs. ?
26. A cubic foot of water weighs 1000 ounces. What
weight of water can be contained in a vessel, the length
width and depth of which are each a yard ? '
n\ "^T "^^""^ ^"""^^^^ ''^'' ^^ P""^ '"^° ^ ^^^ ^ ft- by
0 tt. by -x ft., if a bushel measures 2150-4 cu. inches ?
6
26
MENSURATION.
!■
•v i
An angle is the opening between two str.,m),'f r ./
meeting at the same point. ° ' ''°^' ^^
The siw or ■magnitude of an angle deDenrl, „n, • i
the extent of oveninn «„H „ ,f aepencls entirelyupon
If the two Z rinnilTh "^°", "'! '''"^'* "^ ''« ^"'«
extent of openil ITl T T^ ^ J''"'""""'^''' "^'^
angle willT; I e 1" d'^ t^f ' "^^ f " ^'^'^ °^ '"^
movable and the ot f.;d he siL" ft' '"" "
opening will increase or aZ " °^ "'« ""«'« or
(^) An Obtuse angle is greater than a right angle
0^) An acute angle is less than a right !Jle
When one Ime meets another line so as tn f
square opening or right angle, the one iL Ts idTb'
perpendicular to the other. ^^
A
Area of Parallelograms.
opposrsr:;ran5p:r:u:r^ ''"- '-^^^ ^- -'
Parallel lines are equally distant from each other -.r
every po.nt If produced, they will never mee
a he rails of a ■■ail.oad .-un parallel to eac], other )
pa.tlll!l:. '''''"'''' ^ *"'*- «-' -^ rn.nMd are
(For area of square and rectangle see Book IL , p. 79. )
MENSURATION.
27
Rhombus.
Rhomboid.
A rhombus is a four-sided figure having all its sides
equal, but its angles are not right angles.
A rhomboid is a four-sided figure having its opposite
sides equal, but its angles are not right angles.
1. In the above figures point out the obtuse angles
and the acute angles. Point out two right angles formed
in each by the dotted line. The dotted line is the
perpendicular height, or altitude.
2. The above figures are parallelograms. Why ? Cut
'/rom paper figures of the same shape. Draw the perpen-
dicular height (dotted line) and cut through it. Adjust
l;he piece cut off to the other end of the figure so as to
form a rectangle.
3. This is now a rectangle. Why? Measure the
length and breadth. Find the area. Observe that the
breadth of the rectangle is the same as the perpendicular
height of the parallelogram.
4. How, then, can we find the area of a parallelogram?
Ans. Area = length X perpendicular height.
^ 6. rind the area of a rhombus 12 feet long and 6 ft.
6 in. in perpendicular height.
6. Express in acres the area of a rhomboid 605 yards
long and 32 yards in perpendicular height.
7. Find the he Ight of a parallelogram 3 sq. yds. 4 ft.
36 in. in area and 7 ft. 6 in. in length.
8. A diamond-shaped lawn 53 ft. 4 in. long and 28 ft
in perpendicular breadth is to be sodded. How many
sod*^ '^"'^^ 1 /3 ^„ •■11 1 . - >'
k->, tJctV
;h 16 in. square, will bo required ? (Uratv plan.)
28
•MKNSUlUTfO.N.
B
'HI'
m
Area of Triangles.
fc tnangle. triangle.
A trian^^ie is a figure bounded by three straight lines
l*f ^^^^ M..,/. has a right angle.
An .^.,/«,,,,^ ,,,-^,^^^ j^^^ ^j^^^^ equa! sides
An ^ w.. w^,, has two equal sides
"^ c
Line EB = perpendicular height.
T — = ^ ^>^e BD = diagonal.
parts b, ^:tt:Zo^rt'z:S''r'' ^-'^ ' '^^
kind of a figure ts each ;art ? ° ^'"' ""• ^'''''
a. Compare the two trianelea thii» ^v.^ ■ j
they equal to one another? wla part „f .f" ' , ^'^
gram is each triangle ? ^ °' """ parallelo-
3. What can you say of the si^e «(>„*■ ,
parallelogram having the^ameterL^hTr^'^ ^"'
^"■"",r 7'' '° '^"'^ ">« «^^ °f a trianale
Base, V ft. 2 in.; perpendicular height, 12 ft. 8 in
MENSURATION.
29
e. Tlie base of a triangle is 13-24 chains and its
height IS 8-50 chains. Find the area in acres and rods, 10
aq. cluiina being equal to an acre, t . xC /j;^ ■ <^ ' 1
7. Find the height of a triangle whose area is 27A sq
yards and base 5 yards. . .
8. What is the ])ase of a triangle whose area is 40
acres and i)eri)endicul;ir height 100 rods ? ;' ^ • - •
9. What will it cost to dig a triangular lot of ground
whose base is 45 rods and height 20 rods, at 5 cents a
sq. rod ?
10. What will it cost to fence a piece of ground in the
shape of an equilateral triangle whose sides are 8 rods each
, at 12} cents a foot l^ ' •/ ■ 0 ' c^ ,
J'
Ci*f^"*/'-fOe,
Area of a Circle.
A circle is a plane figure bounded
by a curved line, called the oiroum-
ferenoe, every part of which is equally
distant from a point within, called the
oentre.
The diameter is a straight line
drawn through the centre and termi-
nating at each end in the circumference.
The radius is a straight line drawn from the centre to
the circumference, and is equal to half the diameter.
1. This circli has been divided
into a number of triangles. If the
number of triangles should be
indefinitely increased, what can you
^ ^ say about the relative length of the
side and perpendicular height of each triangle ?
Circle.
I
30
MENSURATION.
'ill
\
^^,J^-^U.t will constitute the sun. of tl^ bases of the
3. Jfow, then, find the area of a circle ?
diviJ^lX ''"''''''-' ^''^^-^^f-'--^ h the ra^nu. and
circltnM'r"''; '^'" ^"•-•"^f«r«"^o nn,l diameter of any
eirclo and divide one ])y the oflior ir /. ^
cli-oter do you <i„., t.:":Li'7 """'' ""'" "'"
6. How fin,! the circmifereiice of a circle 1
Ane MMlpli, th, dmmeUr l>, ;!f „ ,,,, a-U16.
di..l.^ r.l ;^,.-™""f-nce of a drcle whoso
uianiLttr is L, feet ? 4d yards ? 100 rods ?
7. What is the circunifercneo of a circle when the
radius IS ecjual to 2-5 miles ? 7r, yards ?
10. Find tlie urea of the following circles •_
(a) IJimneter, 10 ft. ; circumfercuce', 31-416 ft
g I),,™ete,. 20 feet. (-) ])ia„,eter, 100 feet
11 Fin l,r "',"''• <'■) r.adi„s, 7 ft. 6 in.
;n yard! ""' °' ' "'^'^"'" 1'°"^ ^''»« 'l'''"'«ter is
n,v!^,' ■^'?'' /".'""■"' '""' ■■«'« t*"^ =P"ce covered by a
c.r ,dar plantahon 5(i-.5 rods iu circumference. ^'
^\ 13. What 13 the surface measure of a round tahln
whose diameter is 5 ft. 8 in. ? '®
14 A horse is tied in 'a field by a cord 7i rods in
length,one end of which is attached to a fi.ed Imn
Fmdu. acres and rods the area on which he canlr^e''
13 indf ^'"' "^ ' '""'^ '"^ ^''"^ 'li''"'«ter is
MENSURATION.
D
Solids.
81
n
Cube. i
A Cube 13 asiilid with ■ ■■.| .
SIX eqiiul sciuaru faces. 'J'ri»"gular I'linm. CyUudor.
A Mem is a solid that has two equal and parallel
pa„« %„res for it.s cn.Is. Its si.les are paralleh'^,. Vs
A Cylinder is a round solid having cinmlar ends.
(Book it; ir"''''''''^"'''"''^''"''^''"^"'^'
cylin^defr '^" ^'°" "'"^ "' '""* '"""^"" "^ " P™" «'
Ar^B. MalUply the arm of the. lase hy tlu height.
3. Are these two rules really the same ?
it oui f "''%^~' V"'I'«>^* " 'ri""Sular prism and spread
It out flat Its three upright faees hecon.e a figure of
what kn,d ? Its two ends are figures of what kind ? How
fim tl,e area of its three upright faees ? Of its two bases ?
ui the whole ?
• 6. Ptepeat the above process with a cylinder
cylii?der^"' ' '"^' ^'' '"^'"^' '^' '''" "' " "^^^' P™^ «-
^ • 7. ^l^' ^''^^'V^y i^^^ perimeter of the figure hy its
surface) add the area of the two hoses,
.^ ^ aoxxc by wrapping paper round a wooden model
N'i'
32
i^i
(/
I
T^TFini
MENSURATION.
Find solid content and total area of:
(a) A cube whose side is 6 feet.
(h) A square prism whose base is 2J yards by
2|- yards, and lieight 4 yards.
(c) A triangular prism whose height is 20 feet,
and whose base is an equilateral triangle with sides 12
feet in length and perpendicular height 10-4 feet.
(d) A cylinder whose height is 15 feet and the
diameter of its base 3 feet. ^^
^ 8. What is the upright surface of a cylinder whose
diameter is 20 feet and height 65 feet ?
O. Find the cubic content of a log of wood whose
height is 6 ft. 6 in. and itj diameter 3 feet.
V 10. A cylinder is 3 feet long and li feet in diameter.
How many square feet of canvas will be required to cover
its upright surface ? Its entire surface ?
11. How many cubic feet in a triangular prism the
area of whose base is 920 sq. ft. and height 20 feet ?
12. Find the cubic content of a prism whose heigT fc is
25 inches and base a rectangle 3 by 5 inches.
13. Find the upright area of a triangular prism 5 feet
high, whose base is an equilateral triangle with sides each
30 inches in length.
1^14. Express in cubic yards, feet and inches the content ,
of a cube whose edge is 100 inches.
^16. Ex-^ress in square yards, feet and inches the surface
of the above cube.
j^^l6. How many cubic feet of stone in a rectangular
«^lock 18 inches square at the end and 3 ft. 8 in. long ?
,17. A round tank is 16 feet deep and 8 feet in
diameter. How much will it cost to cement the sides and
bottom of it at 25/ a square foot ?
1 Q TT.,,,r ^.-..-.-.-.,. y^|^|0 £gg|^ q£ ^Q_i_.^jj. ^
XT
-iiUVV iiiU-i
the tank hold
CIRCULAR MEASURE.
83
XI.
CIRCULAR MEASURE.
60 seconds (")
60 minutes
360 degrees
1 minute Q.
1 degree (°).
1 circumference.
For purposes of measurement the circumference of a
circle is divided into 300 equal parts called degrees.
1 . How many degrees in half a circumference ?
2. How many degrees in a quadrant (J circle) ?
3. How many degrees in J of the circumference ? ^
of the cir. ? |- of the cir. ? yV of the cir. ?
4. Through how many degrees does the hour-hand of
a clock move in 12 hrs. ? In 6 hrs. ? In 3 hrs. ? In 1 hr. ?
5. Through how many degrees does the minute-hand
of a clock mo'^^e in 1 hr. ? In I hr. ? In 10 min. ? In 1 min. ?
did
6. In making a journey round the world through how
many degrees would you pass ?
34
CIRCULAR MEASURE.
1. Eeduce 51° 23' 4V to seconds.
2. Ill 20,836" how many dcfTees ?
3. Find f of the circumference of a circle
4. Multiply 67° 23' 17" by 15.
6. Divide 84° 19' 45" by 15.
6. From 57° 4' 29" take 41°* 17' 54''.
7. What is latitude ?
8. If one place is situated 59° north of 'the equator
and ano^ier 34° north, wh.t is their difference in latitude;
9. it one place is situated 26° north of the equator
an another ir south, .Jat is their difference in latSe;
of ^^^^^^^^ ^"T," ''° ''' '^' ""■' -^d that
1 1 Tb 1 . . 1 ; r^'"'^ '^''^ ^^^^^^^^« "^ latitude.
1 1. ihe latitude of London is 51° 30' 49" K nrwi fi. ^-
of New York is 40° 42' 43" N ^J\ ll ?*
latitude. difference in
of 'cle ""oVf '1' ^^ ^"^^^ ^'^P^ ^« ^1° 10^ N., and that
ot Cape of Good Hope is 33° 55' 15" S. Find their
difference in latitude.
B
Longitude and Time.
1. What is a meridian ?
2. rn^t is the English standard meridian ? How is '
It marked m degrees ? Ans. Greenwich 0°
3. mat is longitude ? What is East longitude ?
Wes longitude ? If two places are on opposite sides of
Ldl ""''""' ''" " ^^"^ ^^™ - Witude
4. How many hours does the earth take to turn on'
Its axis, or describe a circumference ?
CIRCULAR MEASURE.
35
equator,
ititude ?
equator,
Ltitude ?
lid that
itude.
id that
3nce in
id that
I their
low is
tude ?
les of
jitude
[•n on*
Bi 24: hours in time = 3G0° longitude,
1 hour in time = — ° longitude.
1 minute in time = £' lon^dtude.
1 second in time = -l^" longitude.
6. How express longitude in time ?
Ans. Divide the number of degrees, etc., hy 15.
7. How express time in longitude ?
Ans. Multijply the nurriber of hours, etc., hy 15.
8. If the difference of time between two places is 19
min. 12 sec, what is their difference in longitude ?
9. If the difference in longitude between two places is
20° 36' 15", find the difference in time.
10. The difference of tune between Albany and San >
Francisco is 3 hrs. 14 min. 47f sec. Find their difference ^
in longitude.
11. The difference in longitude between St. Petersburg
and Washington is 107° 19' 45". Find their difference in
time.
12. Montreal is 73** 25' and St. Paul 93** 4' west of
Greenwich. What is the difference in clock-time between
the two cities ?
13. Montreal is 73° 25' W. and Paris 2° 20' E. of
Greenwich. Fhid their difference in time.
14. How much earlier does the sun rise in Montreal
than in New York,, Ion. 74° ? In Chicago, Ion. 87° 37'
45" ? In San Francisco, Ion. 122° 26' ?
15. When it is 9 a.m. in Montreal, what is the time in
New York ? In Chicago ? In San Francisco ?
(Time will be later in places east ; earlier in places wtsL Why ?)
1 6. When it is 3 o'clock in tlie afternoon at Greenwich,
what will be the time^ in Montreal, Ion. 73° 25' W. ? In
Constantinople, Ion. 29° E. ? In Calcutta. 88° 27' E. ?
Ill
36
PBHCENTAGE.
XII.
PERCENTAGE.
Per cent, moans in every hundred.
Tlie sign of per cent, is %. Tlius, 5/ means 5 nor
cent, or 5 in every liu,„Ired. "^ ^
Percentage i« the process of computing by tl.e Imndred.
coijuter' " ■"""'"■■ °" "'"•=" "- P--"'%- -
^ Jhe ««mfe. 0/ hundredths taken is called the rate per
I. When a num),er is divided into 100 equal parts
what .s one of tl.e parts called ? Two of the paS F^
of the parts? Twenty of the parts ?
2. A man ha,l $500 and lost $10 out of every hun
dred ; how n.„.y dollars did he lose ? How n^Z
cent^? *'"''' '"""'^ '''""Jredths of 100 is 5 ? What per
5. What fraction of 100 is 5 ? Wliat decimal ?
6. Read and verify the following tahle :—
1% = -01
5% = -05
10% = -1
20% = -2
25% = -25
60% = -5
^5% = -75
100% = 1-0
_ 1_
100
1_
i; o
1
1 0^
— . .1,
5
= J
4
— 1
= i
= 1
1
my =
•Vo
I2|% =
«'7i% =
C^'J% =
•^'i% =
617 =
•i/o
8,17 =
I ■ ~ ' --f
•33J =
•GG| =
•125 =
•375 =
•025 =-
•875 =
•0025 =
f
i
8
5
8
i
Jl
TF
1
^
CO
PERCENTAGE.
^
1
^ ^ A (Sight).
1. Read the following deciinuls as rates per cent •—
2. Find the decimal and per cent, equivalent to :—
3. Find the per cent, equivalent to 7 in eyery
hundred; 1 in every hundred; 3 in 20; 5 in 8- Mn SO-
TS in_ 1000 ; 225 men out of every thousand ; 2 in a dozen ;'
uine in a score ; 12 in a gross.
4. Find the fractions (in lowest teims) and decimals
equivalent to :-^
^0% 25% 5% 4% .33^-7 12r/ 8iy
45% 6G|% 4% 4% I75I 325^ l^y -
6. What per cent, is :— ° ° ^
13 cents of $1? 800 lbs. of a ton ? 9 in. of a yd ?
H dys of 1 wk. ? 89 lbs. of 1 cwt. ? | doz. of a score ?
1 qt. of 1 pk. ?
1 pt. of 1 qt. ?
1. J of 850 ■^"-
2. I of 396
3. xV of 550
4. I of 30
6. 1| times 16
6. 2^ times $1.20
7. 2^^ of 1000
3. -5^^ of 2000
9- tV of $4.80
10. f of40
Id. of Is. ?
1 cwt. of 1 ton ?
B (Sight).
•5 of 86
•33^ of 240
•1 of 384
•75 of 20
1-25 times $40
2-5 times $6
•005 of 400
•002 of 500 /
•0625 of 32 '.y
•375 of 64
30 inin. of 5 hrs. ?
1 pt. of 1 gal. ?
50% of 124.
33J-% of 333.
10% of 175.
75% of 50.
125% of 60.
250% of 100.
i% of 600.
i% of 200.
6i°/ of 80-
mx «f 100.
-^7,.
38
PERCENTAGE.
1.
2.
3.
4.
5.
6.
Percentage
35% of 846.
92% of 1004.
1G% of $4.35.
er/o of $1000.
37|%of$1568.
421°/^ of $4820.
7. 9% of $3465.
a 10% of $250.
9. 8% of $600.
^ 10. 257^ of $120.'
11. 6f/^of$320/
12. 20% of $250.
13. 100% of $350.'
14. 6% of 400 men. ^
15. 7% of 300 acres.
20% of 275 gaL
87„ of 50 days.
137, of 300 sheep.
D {Questions 1-10 at sight).
1. In a school of 700 children 10% are absent. How
many are absent ?
2. A teacher receiving $50 a month has her salary
increased 20%. What was the increase per month ?
3. A house and lot cost $4000. The lot cost 37J% of
the whole. What was the cost of the lot ? . •
4. In a school of 600 pupils 66|% are girls ; how many
are girls V How many boys ? What per cent, are boys?
6. My income is $720, 1 lose 12|%. What is my loss?
6. Of a regiment of 960 men 6^% are killed ; how
many survive ?
16.
17.
18.
= Base X Rate.
10. I037, of $34.78.
20. 1137, of 784-1 miles.
21. 47^ of 8-845,
22. 8|7^ of $748.02. /-'
23. 1-17^ of $1477.75. '
24. 17^ of 24900 . .
25. 87^ of -000^
26. 75% of 244 tons.
27. 607^ of 350 marbles.
28. 33L% of 393 eggs.
29. ]6|7^ of 624 soldiers.
SO. 83^7^ of 672 yards.
31. 12|7^ of 848 boys.
32. 37^7, of 960 rods.
33. 87|7, of 800 bricks.
34. J7o of 690 oranges. ^
35. 17^ of 500 bushels/--
36. 1207, of 60 lbs.
PERCENTAGE.
39
V
7. I had $750 in the bank and drew out 4% of it.
How much was left ?
a A town of 10,000 inhabitants increased 25% in 5
years. Find its population. -^' \
/ O. In a sclmol of 300 pupils 7% study ,Latiii, 15%
yAlgebra, 66f^^ench and 75% Arithmetic; 'How many
pupils study each of these subjects ?
iO. I have 40 cent-pieces, 20% more quarters than
cents, and 8J% more dollars than quarters; how many
dollars have I ?
i
•w
11. I had $875 in the bank and drew out 15 per cent,
of it ; what remains ?
12. In a village containing 330 people 13yV per cent
are under 10 years of age. How many are under 10?
What percentage are 10 or over ?
13. Which is greater, 7% of $6300 or 6% of $7200 ?
14. A farmer raised 5972 bu. of grain and sold 65 per
cent, of it at $0.65 per bushel. How much did he
receive ?
15. I spend 18f per cent, of $950. How much have
I left ? 1/^
16. If I buy a cow for $64.50, at what must I sell it
to gain 10 per cent ?
17. The prime cost of some goods is $3.75; for what
must they be sold so as to gain 15| per cent. ?
18. I buy a fariii for $2225 ; for what do I sell it if I
lose 8 per cent. ?
19. What is 11 per cent, of £10. ?
20. What is 55 per cent of 12 cwt. 90 lbs. ?
21. The population of a city in 1880 was 100,384.
During the following ten years it had gained 113 per
cent. ±md its population in 1890.
w
40
PERCENTAGE.
XIII.
A (iiiyht),
1. What fraction of
4 is 2 ? 80 is 15 ?
12 is 6 ?
20 is 5 ?
Jb is 50?
100 is 3?
100 is 25 ?
100 is 89?
60 is 40 ?
2. What per cent, of a number is tlie whole of it ? I
of it? iof it? I of it? l of it? J of it? 4/ §?
3. («) What fraction, {h) what decimal, (c) what
per cent, of
20 is 12 ?
25 is 12?^
25 is 7 ? ■
200 is 50 ?
25 is 5 ?
15 is 6 ?
10 is 3?
25 is 15 ?
2 is J?
2 is J ? ,
3 is I iy^^({ •
What per cent, of
1. 100 is 12p
B (Sujht).
2. IGfisO?
3. 3:.]^ is 10?
4. $300 is $12 ? :
6. $450 is$90?o^^
6.
7.
8.
0.
10.
i is I?
Is. is 4id. ?
66 days is 11 days f
66 men is 6 men ?
2 days is 8 hours ?
$1 is 6| cents ? 4,
•i'
11. I had 400 sheep and sold 120. What per cent, did
I sell ?
'Vo ^^i''^
12. I had 400 sheep; I now have 500. What is the
per cent, of increase ? >0^/ o '^^-^
13. I had 400 sheep ; I now have only 260. What per
So'cent. of decrease ? What'^er cent, have I left ?
14. raid $25 for a chest of tea and sold it for $6 more
than I gave ; what per cent, of profit ? ^--'i «, ,
w*
[
what
'D'"."
■/
PERCENTAOa
41
16. Bought a horse for $25 and sold him for $50; what
per cent, was tht profit? /' ^^''■\,
16. I lose J of my money. What per cent, still
remains to me ? r
17. If a pint of water is added to a gallon of milk, what
per cent, of it is water ? ' /
18. I lost 16f% of my money; what per cent, had I
left? 'c'<3'-^"
10. 40 marbles; gave away 15 ; wliat per cent, did I
V^glve away ? What per cent, did I keep ? /.-i' r
20. 6 oranges in a box containing 5 dozen are bad;
what per cent, are good ? '
Bate = PevQentage -j- Base.
1. What per cent, of 2. What per cent, of
n is 2f ? '. ; , :^ 63 miles is 10-08 miles ? / ^
$5i is $4f ? -^<6 I „j ^ 154 lbs. is 7 lbs. 11-2 oz. ? J '
S420 is $60 ? , ^ ti. 4yds. is 9 inches ? U {;
$1600 is $96 ? /, ^ 142 yds. 8 in. is 32 yds! ? ^ ^1-
3. If 24 apples are spoiled in a barrel containing ^^
288, what per cent, is spoiled ? j ^
4. In a school of 180 pupils 153 pass an examination ;
what per cent, fails ? ' - °/o
6. If the rent of a house is reduced from $375 to
$350, how much is the reduction per cent. ? L '-:
6. If the rent is increased from $425 to^$459, how
much is the increase per cent. ? %
7. How much per cent is Is. 6d. in the J^l. ?
r
^ 8. I pay $1 for a book of which the published price
IS $1.2© ; what per cent, is the reduction ? / /^ f"
O. From a cask containing 90 gal., 4 gal. 2^qts. leaked
out; what per cent, leaked out? -$"
8
^
*2 PKRCENTAQE.
10. In a vilk^cre containing 2088 people 87 die of fever-
what is the death rate per cent. ? ^ ^ '
1 1. To 72 gallons of milk 3 jrallons o^ water are added;
what per cent, of the mixture is water ? /
12. An article bought for $2.50 is sold for $2.75 ; what
is the gain per cent. ?
13. If I gain 1^ cents on every 12 cents, what do I
gam on the dollar ? > ^ ,
14. Bought eggs at 16 for a quarter and sold them at
lu tor a (piarter ; what is my gain per cent. ? -^ - -
15. A fruit-dealer bought oranges at 25 cen^sl score,
and sold them at 25 cents a dozen ; what did he gain p c ? -
16. If I buy at 30 a dollar and sell at $0.75 a dozen
what IS my gain per cent. ? '^ ' .
17. In dictation I spell 235 words correctly out 5f
250 ; what per cent, of the words are correct ? '/ ^
18. What per cent, of 75 bu. 3 pk. are 50 bu. 2 pk ? ;
19 Sugar whicli cost $4.37^ a cwt. is sold at the rate
ot JO lbs. for a dollar ; what is tlie gain per cent. ?
20. If the population of a town increases from 8624 to
9702, what is the increase per cent. ?
/^c;
XIV.
^^. ^H
A (Sinht). s
1. 8 is J of >vhat number ? |? J? |? 4^
2. 24 is 1 4)f what number ? f ?^^4 ?^ « u A ?^'^ jl ? a t)
3. 12 is 507^-of what
307^'' 407^y 607^^'
number? I07 ? 207 ? 257 ^
707^ f 757.1° 807jr 1007 V (^'
. i. 1 n t a I ii\ ^ ■. r\ , - i> _ _ .
4. 16 is I7i of what number? A7 '^ "4-7 ?'' V/ ?
PEKCENTAQE.
43
Find tlio nuinl)er of which
6. 48 is 07^.
6. 24 is 47°
7. 32 is 5°/°
8. 48 is 20°%.
O. 12J is 107^.
10. G| is 257/
11. 5 is 8iyJ
12. 50 is 62l7^.
13. GO is 607,"
^14. i is 16i7°.
B
15. J is 507^.
16. 20isr/o.
17. iif;40 is 207^.
13. S(58iH;u7°
19. 25 (!(,.;. is l'2f /^.
20. 15 is 1257^.*'
21. 750 mi. is 507^.
22. 40 yds. is 57^.°
23. 75 is lG6f //
24. 15 days is 17^.
'.V^
2x^" Base = Percentage -f- Hate,
1. 85 is I of what number ? />J ^
2. 225 is -025 of wliat number ?
3. 555 is 62^7^ of what number ? -
4. $495 is I of what sum ? 1807^ of what sum ? '^ ^ ^
6. $9820 is 85 per cent, of what sum^^^.^— | j j . .X- ^
6. 210 tons is G07^ of what quantity ? :,• " '
7. £2000 is 11 5 per cent, of what sum ? 173^^. '
a. $873.25 is 4^ per cent, of what suip ?^ ./ ,^ ^^•''^ ^^'-j'
0. $476 is I per cent of what sum ? ^ •, b o'^-o o '
10. $175,420 is 11217^ of what sum? '" ' i c? >S ,<i ^. ^
C (Questions IS at sight).
1. A scholar has 18 examples in arithmetic correct
which is 757^ of the whole ; how many examples given ? '
2. In the ten years ending 1890 a city increases 8000
in population, a gain of 25 per cent. What was its popu-
lation in 1880? ''.-.'- ^
3. Butter is sold at 25, cents a lb., which is 2007 oi
Its cost. Find its cost. A^^
4. I spend $1200 or 807^ of my salary; what is my
salary ? ^ ' . ' ''
44
PERCENTAOE.
6. Tsell fi horse for $00, which is 120°/^ of its cost;
what (h(l it cost ?
^ 6. The nmiil)cr of chihheii nttcndinj^^ school is 862 or
20% of the i)opuliitiou ; what is the j)oi)uhiti(Mi ? J-j ^'/ J
7. A house was sohl for $6300 or 250 per cent, of its
cost ; what did it cost ? -i j '
8. 4% of 2;J0 l)u. is 57^ of what quantity? > 9 ^ rho
0. 12r/^ofr>30is6|7^ofwhatsum?/y /; ■
10. 8ohl Roods at a piiii of 227^. The profit was
$47.80. For how much were they sold ? ^ i* -^ \ •- ' ,
XV.
^ A (Sii/ht).
1. 10 is I more than what nund)er? -25 more? 257
more?
2. 10 is J more than what nund)er? 3.3^7 more?
3. 8 is 'J less than what number? | less?
4. 70 is 12^7o ^^''^^ <^^»'^^i what numl)er? 507 less?
6. 36 is 12r/o more than what number? 10°/ less?
6. What number increased by 257^ of itself is°100 1
7. Wliat number increased by 6|7 i« 08 ?
8. What num1)er increased by 25°/ is 35 ?
9. What number diminislied by 207^ is 60 ? Is 48 ?
10. What number diminished by 307 is 70? Is 49?
11. A horse was sold for $40 which°was 33^7^ more
than his cost ; what was paid for him ?
12. A jeweller sold a watch for $110, gaining 107
What did it cost ? ^°'
13. A pupU answered 24 questions correctly, which
was 207o less than the total number. How many ques-
tions were asked ?
14. A pig cost $21, which is 16|°/ more than the price
nf n. nnlf "Fhul fhp Torino f\f o oolf/ii '
)
fl.-i
PERCENTAGE.
45
B
10%.
What number incroasal What numlxir diminished
1. liy 107^ is $2750 US<^ e. By 1^7^ is 5100 9^ ^^'
a. By 107^ is $i)r,r,2 ? ^^.^^ 7. By Vr/' is G475 't^y „^^
3- % 207^ is $.S720 ?^. ^ 8. liy my is 13125 ?^. -v^)
4.
By 28^7 Js $8095 ?7^- 0. By 67 i« 2100?^
*. J /y
^ ^ ^^y,':^Vo ^'« *»«-«0 » '^'^■•'^^ 10. By 127^ is 1200 ?''*** V'
11. My flock of shoep in^jreased 8 per cent.; I had
then 324. How many Imd I at first? S^^ ' ol-v>^
12. I lost 8 per cent, of my flock of sheep and had 276
remaining. How many had I at first? ^<' t-
13. A town after decreasing IV /^ has 4539 inhabitants.
How many inhabitants had it at first ?oV^i)
14. If after decreasing 22 per cent, the population is
ii003, what was it before the decrease ? J" ^^"5 -'
16. What was the original price pf a book sold for
$1.20 at a loss of 36 per cent. ? /^ h 7-£
nolo' ^Z^'"'' i"creasing 11 per cent, the population is
5883 ; what would it be if it has decreased 11 per cent. ?>2'V'
17. What percentage of a regiment survive, if ^ die m
battle, J of their wounds, and ^ of fever ? ? S i /
/ 18. A shepherd loses J of his flock and then 207 of
the remainder, and has 384 left. What was the original
number?:' \tiu^J^.iJ^, (1^^
10. By selling 500 sheep for $2695 I gain 10 per cent •
(^ what did each sheep cost f/'^ >9 O
^^ 20. I lose 207^ of my money and then 12^7 of the
remainder, and have $2240 left; how much had {^^"^^^
, 21. Of the eggs sold by an old woman 3f per cent, axe
bad and 154 are good. How many were sold ? v ': ^ -^JT- :
22. A grocer sold 950 barrels of flour for $5760, which
was 207^ advance on the>st ; what was the entire cost
^7
.9^
and the cost per barrel ? ,t5
I
'■^
yi (-4- i <ro cxA^b 3
PERCENTAGE.
XVI.
«'
PROFIT AND LOSS.
The difference between the buying and selling prices is
called Profit or Loss, according as the selling price is
more or less than the buying price.
Profit and loss are calculated by perOentage.
The cost is the hise.
A (Sight).
What is the selling price in the following cases :—
1. Cost price $100, {a) 5% profit, (h) 10°/^ loss?
2. Cost price $500, (a) 10% profit, (h) 2Q\ loss'/
3. Cost price $20, {a) 20% profit, (&) SOV/loss?
4. Cost price $129, {a) 40% profit, {h) 50% loss?
What is the profit or loss 7^ in the following:—
5. Cost price $200, («) $20 gain, Q,) $20 loss?
6. Cost price $600, (a) $30 gainV(&) $100 loss?\^"-*
7. Cost price $40, («) $5 gain, {h) $13^- loss?
8. Cost price $500, {a) $5 gain, (?>) $10 loss? ^"^
0. Goods sold at double the cost ?? 1 J times the cost ?
Wliat was the cost price in the following :
10. Selling price $120, {a) 20°[gkm, (b) 20% losstc^'
1 1. Selling price $150, (a) 25% gain^ (b) 25" f loss?"
12. Selling price $300, (a) 50°/^ g^indh) 50°/ loss? ^o^
__13.^elling price $140, (a) 40% gain, (5) 307° loss % ' ''
14. I buy a cow for $25 and sell her for $30. What
have I gained per cent. ? ^^^fo
15. Sugar costing $150 is sold for $165. Find the
gain per cent. ) 0 ^^
N
16. If the gain on $9 is $2, what is the gain 7 ?
J
f
PERCENTAGE.
47
17. Bought goods for $25; for how much must they
be sold to gain 8 per cent. ?^"\
18. What must a table. costing $57 be dold for so as to
gain 5 per cent. ? si -CiS '
1 9. What nmst be the selling price of goods which cost
$32 to yield 25°/^ profit ?"^ HO
20. If the gain on $24 be $3, what is that per cent. ? J:^
^21. A person bought goods for $64 and sold them for ^
$72 ; how much was gained per cent. 1/^^
22. A picture costing $75 was sold for $60. Find the
loss per cent, ^-o V,,
23. By selling goods for $5, 25% is gained on the cost
price. Find the cost price.
24. Selling price $48, gain 20%. Find cost price. V (^
26. Selling price $48, loss 20%. Find cost price. -^^^^ <5
26. Cost price $80, selling price $60. Find loss p.c.^ 5 1^
27. Cost price $10, selling price $12. Find gain p.c. . ^ '
^
B
1.
2.
3.
4.
cy
Cost price $96.50, profit 67^. Find selling price. ' f^^^ ^ ^
Cost price $2750, loss 35%. Find selling price.)7 ^V^'^ i
Selling price $675i, profit 10i%. Find cost price^r ti'M
Selling price $2750, loss 157^. Find cost price.. ^^:->i^
6. Cost price $3584, selling price $4175.36. Gain 7 f
6. Cost price $8500, selling price $6970. Find loss % / &fi,
7. If I lose 5 per cent, by selling a watch for $47.50,
at what must I sell it to gain 8 per cent. ?%-// , qq
8. If I lose 8 per cent, by selling a machine for $23,
at what must I sell it to gain 157^. ,5 §'76'^
9. If I gain 10 per cent, by selling for $45, how much
per cent, should I lose by selling for $36 ? /(^ ^/o
10. If I gain 8 per cent, bjr^^selling for $63, at what
must I have sold to lose 167^ ? ^'/jl Q
43
PEBCENTAGE.
m
11. If I lose 10 per cent, by selling at $40, how much
per cent, should I gain by selling at $52 ? ' =:/
12. By charging $15.75 for an article 5°/^ is gained;
how much 7^ would be gained by charging $16.50 ? / 0%
13. Selling cheese at 16| cents I gain 10%; at what
mu.§t I sell it to gain 20 per cent. ? ; i v'^
^14. By selling an estate for $15,000 a man gains 20
'per cent. ; how mucli did he give for it ? > ' c) ;: »> •'•
15. By selling an article at a profit of $2.50 I gain 16
per cent. ; what did I give for it ? r ^S, h ;> -
16 Sold goods at a loss of 20% and ac'tual loss of
^o / .50. Fmd the prime cost. ''' ^ p J. j .
17. What is received for 30 yards" of cloth costing 55
cents a yard, when sold at an advance of 20%? /f, ^6
18. Bought apples at 3 for a cent. ; how many can be
sold for 5 cents to gain 6f per cent. ? '' ^ //,
19. A merchant sells 95 bags of rice L $35f, thus
gammg 12J per cent. ; find the prime cost per bag;/^
20. An agent sold a lot of ground 25 feet front by 75
feet deep, at 80 cents a square foot, and charged the owner
2 /^ of the money received for his services. What was
the agent's commissionitp What did the owner receive ? ¥
.- 21. A commission merchant sold 150 barrels of flour
\^ at $5.80 a barrel ^nd charged 4% commission. What was
" his commission ? ' -^ - ' ' ^ ^
22. A commission of 57^ is charged by an agent for
collecting an account of $49.80 \ what sum does he pay to
his employer ? /M ' J /
23. If $420 are paid annually for insuring a property
for $18,000, what is the rate per cent. ? ^- >
24. If $72 are paid for insuring $4800, what is the rate ? / '
25. How much must be paid for insuring a store and '
goodsvaluedat$7500, if therateis ir/ ? i « - ^
y\
\
INTEKEST.
49
JOf^
by 75
)wner
b was
flour
t was
perty *
rate?/'-^ >>
and
XVII.
INTEREST.
Interest is money paid for the use of money lent.
Principal is the sum lent.
Rate of Interest is the rate -per cent, of the principal
payable annually.
Amount is the sun^ of the principal and interest.
A {Sight).
1. If the interest of 100 is $6 for a vear, what would
be the interest of $50 for the same timel-^ Of 200 ?^'' Of
$300 ? Of $400 ^ V Of $150 ? Of $250 ?
2. If $6 is paid for the use of $100 for a year, how
much should be paid for 6 months? 3 months? 4
months? 8 months? 9 months ? 1 month ? 11 months?
3. What part of a year is 6 mos. ? 4 mos. ? 3 mos. ?
2 mos. ? 8 mos. ? 7 mos. ? 9 mos. ? 10 mos. ? 11 mos. ?
4. What part of 1 year's interest is the interest on the
same sum for 1 mo. ? 2 mos. ? 3 mos. ? etc.
5. Reckoning a month as 30 days, what part of a
month is 15 days ? 10 days ? 6 days ? 5 days ? 2 days ?
6. If the interest on a sum of money for a month is
$24, what is it for 15 days ? 5 days ? 3 days ? 20 days ?
7. What is the interest |or 1 year at 5% on $100 ?
$300? $500? $450? $50^ $1200 1 ^^^
8. What is the interest; for 2 years at 5% on the
above sums ? ■ yi( i -^ , -a
O. Interest for 2 years 6 mos. at 4% on above sums ?
10. Interest for 2 years at 3|°/„ on the above sums ?
60
INTEREST.
B
1 1
Interest
\l
'^^icipal X Hate x Time,
(Express rate decimcdhj, e.g., 6% = j§, = -qq,^
Find the simple interest on :—
1. $627 at 5 per cent, for 2 years.'^/, i • > o
2. $203 at 6 percent, for 3^ years >. ^ ,/ ^
a $910 at 5^ per cent, for 3 JeZ ^
4. $825 at 3^ per cent, for 31 years. ^ 5^ t^
5. $/7o at 21 per cent, for 4 months.^ ^?^5 y i
6. $64 at 4| per cent, for 15 months. A3 /^ ^
7. $607 at 4 per cent, for 7 years, y ^^ ■
- 8. $144 at 1} per cent, for If years. '5 . VI U
0. $510.62^^ at 4 per cent, for 4 years X ; 1 ^
13' «20- 9. ll ?f •=""' '""^ " ^'^"'^ 2 month. Tilt
13. «20o.25 at 5-75 per cent, for 18-375 years.^^" I « i • 3 J:
W900-875 at 4-45 per cent, for em~i '.' ' ?A"
$280.14 at 3-86 per cent, for 5-19 yeaJJ.^^ ' ^ ' " '
18. $3000 at IrV per cent, for 1 year 11 months. ■" ''
Tind the shnple interest and amount of :_
19. $248.60 at 6 per cent, for 3 months.' ?■ •) p i
20. $275 at 6 per cent, for 2 months. ^ 1 y
21. $5000 at 5 per ce5it. for 1 monthji' SVr .
$2835.20 at 6 per cent, for 2 months.
$850 at 6 per cent, for 73 days.
$«70 at 5 per cent, for 146 days.-:
<tt ^ O K 1. I-T *
14
15,
16.
22
23.
24.
^25.
26
27
►. $'7H5 at 7 per cent, for 219 days. ■
>. #1^ ) at 5 per cent, for 75 days. '
. f 3c 75 at 6 per cent, for 130 days:
INTEREST.
M
28. $1864 at 7 per cent, to- 2 yrs. 245 days. 3 ^^^ ■ ^ ^
29. $1G84 at 6 per cent, for 1 yr. 280 days, i, / y^-:. -'
30. $0500 at 7 per cent, for 3 yrs. 73 days. / / Lj ) ; . u b
31. $1156 at 7 per cent, for 219 days. -^ ^''^ ' -^^'
^-32. $4470 at 4 per cent, for 292 days. - 7^ J. 6 t/ .
33. $1250.26 at 6 per cent, for 1 yr. 146 days.X'"*:> '^'
Find the interest, reckoning even months only, of:
/ 34. $165 at 6 per cent, from Jan. 4 to April 4, 1890.
v/35. $270 at rijxota June 19, 1890, to Apr. 19, 1891^^. ) y
^36. $1234 at ^1^ from Apr. 10, 1894, to Oct. 10, 1894:' ;, cv
v/37. $1895.23 at 6% from June 25, '88, to Mar. 25, '89; <<5 ">
/ 38. $560.60 at 7% from May 5, 1891, to Dec. 5, 1892.
y 30. $275 at 6% from Jan. 12, 1893, to Nov. 12, 1897.- '
Find the exact interest of : —
40. $100 at 5% from May 1 to Aug. 10.
41. $500 at 4% from April 2 to June 4.
42. $1375 at 37^ from Dec. 1, 1890, to May 1, 1891. / 7- ^ i-
c^Z, $4596.50 at 3% from Dec. 30, '91, to Mar. 31, '92. '
44. $1200 at 3% from Jan. 3 to March 15. 7. ^: , -
45. $4380 at 3 J7o from Dec. 3, 1885, to Mar. 21, 1887.
//46. $3625 at IJV^ from Oct. 2, 1885, to May 17, 1887.
C
Bj(d6 = Interest ^ {Principal x Time).
(This will give rate expressed decimally. )
1. (Sight) At what rate of interest has the principal
been invested in the following cases : —
If $100 in 1 year gives $10 interest ? $7 ?
If $500 in 2 years givfes $60 interest ? $25 ?
If $200 in 3 years gives $24 interest ? $60 ?
If $250 in 8 years gives $25 interest? $150?
If $400 in 3 years gives $60 interest ? $45 ?
If $200 in 2| years gives $30 interest ? $135 ?
^
52
INTEKEST.
'■'' I
;i
Find the rate of
iterest : — u^
2. When the interest on $700 for 8 yrs. is $168. ^ ^
3. Wlien the interest on $375 for 4 yrs. is $56.25.^ J/
4. When the interest on $956 for 2i yrs. is $119 50 <3' "
^6. When the interest on $1421 for 7^ yrs. is $355.25. J i
6. A\hen the interest on $1000 for 12^ yrs. equals ^
the principal V ^ ^
7. When the interest on $300 for 9 mos. is $18. §
^-^. When the interest on $8450 for 3 mos. is $147.87} 7
O. When the principal doubles itself in 5 years. r>D '
10. When the interest on $652 for 15 years is $440.10. Vi
1 1. When a sum of money is doubled in 16 years. , '^'
12. When the interest on $1728 for 3 months is $84. % -"
13. When an investment in 5 years yields a sum ^
equal to | of the principal. 6^ V,
14. When $490.62} amounts to $686.87} in 8 yrs. 6'^)
15. When $500 amounts to $562.50 in 4 years jl )
16. When $105,700 amounts to $116,270 in 10 ylars*^ i eJ
17. When $213.50 amounts to $266.87} in 64 years u. ^ "
18. When $328.80 amounts to $356.20 in 2 years ' u' '
^ 19. When $311.50 amounts to $336.42 in 1 yr. 4 mos"^
//
L
Time = Interest -^ (Principal x Hate).
(Express rate as a fraction, e.g., .5% = ^s^.)
1. (Si^hf.) For how many years has the principal been
earning interest in the following cases:—
$20 interest, $300 principal, 2°/^ rate ? 3°/ ?
$90 interest, $400 principal, 3°/° rale ? 5°/ ?
$48 interest, $400 principal, 4°/° rate ? 6°f ?
$45 interest, $450 principal, 10°/^ rate ? 2}-°/ ?
$60 interest, $200 principal, 2}°/° rate ? ny° ?
$250 interest, $5000 principal, 2}//^ rate ? '^ 4°/ ?
INTEREST.
63
Find the num})er of years in which : —
2.
3.
4.
6.
l^
The interest on $1100 at 3f /^ will be $115.50,
The interest on $1250 at 6°/^ will be $1^7.50. - -^
The interest on $390.62^ at 4% will be $46.87J.3
The interest on $4209 at 5% will be $52.61i. 3
The interest on $750 at 4% will be $20. -T /^
7. The interest on $50 at 5% will be $100. ^ b^
The interest on $840 at 21% will be $161.70. 7
The interest on $4212 at 4i% will be $277.87|.
$4900 will amount to $5292 at 4°/^. ' ^
$210 will amount to $252 at 21°// 7
A sum of money will double itself at 3^/^. ^ ^ "^^
$50 will amount to $85 at 6%. '^ ^
$1650 will amount to $1782 a°t 4%. "s^
15. $3745 will amount to $3932.25 at 2|%.-^
16 $2416 will amount to $3050.20 at 5|7°.^ ^
IV. $500 will amount to $606.66f at 51°// ^
c-^ 8.
9.
10.
i-ll.
12.
13.
14.
Principal = Interest -f {Rate X Time).
(Express rate as a fraction, e.g., 5^% = WVV-)
1. (Sight.) What is the principal in following cases?
Interest $100, rate 1°/^, time 1 year.
Interest $450, rate 57^, time 2 years.
Interest $300, rate 2|7^, time 6 years.
Interest $300, rate 37^, time 4 years.
Interest $60, rate 117^, time 2, years.
Interest $270, rate 37^ time 2 years.
Find the principal which will produce : —
2. $63 interest in 3 J years at 4 per cent^ d ^
L^3. $60.12 J in 5 years at 5 per cent. ^^^^' <>' ^
4. $70,31 J in 3 years at 6 per cent. 3 '^
6.
Jf
2.50 in 5 years at 2 J per cent.^ o-d , ir'i^
^-€: $101.50 in 71 years at 3i per cent.^ ^- ^^
64
Hi
INTERKST.
I>
7. 6 cents a day at G% per annumf ji" ^ J-
8. $4r>0.G6 ill 3 yrs. G mos. at G7>' ^ ///^
Find the principal which will miunmt to:—
O. $5292 in 2 years at 4 per cent? u '^ trO
10. $2G7 in 2} years at 5 per cent.
1 1. S55G.25 ill 2 yrs. 3 nics. at 6 per cent. .$ <ru
12. $;]G4.G8i ill 5 yrs. 9 nios. at SJ per cent. ^^^
13. $221.07 in 3 yrs. 4 mos. at 7 per cent.'^/ ■- .y
^4. $286 in 3 yrs. 4 mos. at 9 per cent. ■ y o ^o
^\^' f!f:'-^-^^"^3>^-^-6n.os.at4percer^.J ^., .
16. $287.50 m 2 yrs. 6 mos. at 6 per cent. 'O ^o.
/ Problems in Interest.
1. Find the amount of $140.G2J for G years 73 days
at 4 per cent. / ; -', ^-^ ^
2. In what time will $1263 double itself at 4i per
cent, yearly? ,-; . - c^>j ^^
3. At I per cent, monthly, find the simple interest on
5lf2a for 1 year 11 montlis;'^,:* . / j- -
4. In what time will $370 gain $123,334 at 3i per
cent, per annum ? r '^
11 ^* "^i""^ ^^'^ ^"'''''''* °^ '"^^^^^^^ ^« ^e paid on $200 for
11 mos., $250 for 9 mos., and $300 for 6 mos., at 5°/ - ^ y^
\^<,%f^'''of ''^' P'' "'^^- ^'^^ '^'0.95^ amount to/
3P7«.()OiV in 3^ years ? ? ^
<.QoJ\n^^ ^I"" ''''''''"'^ ^^ ^^^ ^"^ ^^ 4 «^o»ths at 2^7 is
^JJ2.40, what was the principal ?* ? -
^o, o"ro-^^ *1'^ ^''^''^ "^^"'"'^ ^^^'^ ^ y^^^rs at 4 per cent, is
3^ol.J0g, what was the principal? // ., ,
9. Ill how many years will the interest on $G90
become $87.97i at 3 per cent. ? -
10. A professorsliip was founded with a salary of
$1250 a yr. ; what sum was invested at G7^ to produce it ? Xo- H-
h
U'
INTEUKST.
65
1 1. A man has $8000 wliioli ho wishes to invest so as
to proihice $500 a year ; wli.at rate inu.st he cliarge ? <> .^ ^^
12. At wliab rate of interest must $450 be loaned to
gain $50.50 in 1 year 6 months? ^ V t /.
13. What sum invested at 1% a month will amount to
$500 in a year % ^ -' - ^/ : , '
14. How long will it take $350 to gain $1350 at 6°/ ?/^ - h.,j
15. Find the interest o| $150 from January 1 to^ ^"^
November 20 at G per cent;'/ , q ^
16. Find the simple interest of $000 for 93 days at 6
per cent. -
17. Find the interest of $420 for 73 days at 47'^.J'<^
18. Find the interest of $1425.20 for 219 days at 3
per cent.
1 0. What is the interest on a loan of $5800 from Jan
15 to July 4 at 0 per cent:t / & .J ■ .^ '^ y
20. A girl is 1 9 years old. What sum of money must
be invested for her at 4% simple interest, that she may
receive $405 when she is 21 t'S ^6
21. January 1, 1894, $036 was put out at interest. On
September 1, 1895, it had amounted to $078.40. Find
the rate of interest. V -4
22. On May 1, 1890, $300 was borrowed at 21°/
interest. It remained on simple interest until it amounted
to $405. When was the debt paid ? ' ,.^v^i J, , y:
23. A certain sum of money was placed on simple
interest at 4% when a child was born. In 25 years it
had amounted to $520. What was the original sum ? j
24. When was $500 put at interest at 5^0 if on July
1, 1894, it amounted to $G00.00|? ./^^-; • / > '
25. How much must be put at interest at 5°/ to have
a monthly income of $100 (^ A daily income of $5r.> ■ ^
\X-,
i K.i>^.'j^
66
DISCOUNT.
XVIII.
DISCOUNT.
Diooount is a deduction from n stated price, or from a
debt paid before it is due.
Bank discount is simple wtrrcst paid in aihance.
Wliolesale business bouses usually sell goods on time
and take notes from tlie retailers in payment. Wben tbe
bolder of a promissory note sells the note to a bank the
sum paid by tbe bank is called the proceeds of the note.
I lie amount deducted from the face of the note is the
discount.
$000.
Montreal, ^r)th January, 1896.
Forty (Jayfi nficr date Ij^romise to pay Gault
Brothers or order nine Imndred dollars, value received.
Diseounted at cy^, Feb. 4th. JOHN MARTIN,
»
Who is tbe maker (,f tbe above note ? Who is the
payee ? What is the face of the note ? Is the note
negotiable ? K\^;
rind the da^y on which it will mature, allowing 3 days'
grace. Who discounted the note ?/ How many days had
thejiote still to run when it was discounted ?
Find the amount of discount which tbe bank will
deduct from the face of the note.
rind the proceeds of the note. To whom paid ?
Who will be responsible to the bank for the payment
of the note at maturity ?. -If the note is not paid, what
must the bank do ? -^ ^ %h/^
t
.A
DISCOUNT.
67
Bank Discount.
1. Find the day of maturity of the followiTig notes, the
date of the note and time being given: —
Sept. 7. Time, .M mos. ' ISfay 18. Time, 6 mop.
Anglo. Time, 4mos. Nov. 20. Time, 11 mos.
July 27. Time, 5 mos. i May ^0. Time, 13 mos.
2. Find tlie day of maturity of the following notes,
reckoning exact days : —
Feb. 10. Time, 10 days. '^June 7. Time, 47 days.^
Kov. 23. Time, 20 dafs'/^ April 0. Time, 70 days.'
Aug. 10,. Time, no day's/' _;,^ July 3. Time, 60 days.
3. Find the number of days that the following notes
have to run from date of discount to date of maturity:—
Date of note, Aug 3. Time, 3 mos. Discounted Sei)t. 15. ^
Date of note, July 7. Time. CO dys. Discounted July 7.4 j ..
Date of note, Sept. 15. Time, 4 mos. Discounted Sept. 21. ; ; ^^
Date of note. May 21. Time, 00 dys. Discounted M.ay 20. f y /
Date of note. May 30. Time, 30 dys. Discounted June 15. / ; i'
Find the day of maturity, the bank discount and the
proceeds in the following cases :-^ t> u^j/ ^ ^ - 1 5 '» ■ .^1 ^*
4. A note for ^SOO, dated Feb. 11, 1801, and due in
3 months; discounted two days after date at 7%.'
5. A note for .$576, dated Oct. 3, and due in one
month; discounted Oct. 12 at (f/^j/auo^l'A^ <tf ''r'l^ <^(^
6. A note for $720, dated June 12, 1895, and due in
60 days; discounted July 1 at ^"/^.Oxi'^ T ''l '5 '/iJ>/6' '
7. A note for $^000, dated U March and due in 3 ^^
mos. ; discounted at da.^e at 0%. , , v. • !(. \'i •(.( ^^ C{Vj ■{ ' '
8. A note for $300, dated Oct. 14, and due in 90
days; discounted Nov. 4 at 10%. Fill out this note from
yourself to George Ross as payee. • . c- jl SQ. %
'^P'
n ,
o >■
4 5„
I
68
DISCOUNT.
O. A
inorchar
s custoinor
sold ^'oods to the
amount of $:U0,
tt amount due in 3
months witliout interest. Ho immediately had the note
discounted at the bank at G%. What did he receive f ^ '
10. A merchant bought $G800 worth of goods for
cash. He sold them at a profit of 15 per cent, agreeing
to accept Ins customer's note due in 4 months. He
immediately had this note discounted at the bank at 67
Find (1) the face of the note, (2) the proceeds of the note!
(.3) the merchant's profit. '- ■ -^4 "7 f U .Sj Y 'ifC >■
1 1. Walter Green bought some goods from Peter Smith
on JMarch 15, 1895, giving in payment his note for $500
due in two months without interest. Write out this
note. Smith needed tlie money and had the note dis-
counted on the day it was dated. H the rate of discount
was 7 /^, what sum was received by Smith ? Suppose
Smith had kept the note till the end of April, and then
discounted it, what would he have receivedl a-)
•a. H
^4
H-'
Trade Discount. M ^ ^ . ' ^. -. ^
1. A tradesman allows a discount of 5 per cent, for
cash ; what is the cash payment on ^n account for $210 ?
2. A tradesman allows a discount' of 15 per cent, for
cash. Find the cash price of articles marked $5. S3 50
$1.12J. - J ■ •ff',^.ou,
3. What reduction shall I get from the price of a
book published at $1.25, when the bookseller deducts 10% ?
4. The list price of a piano is $480. A trade discount
of 33J per cent, is allowed and a further discount of 5
per cent, for cash. What is the cash price ?
\
/
c
L
PUESENT WOKTH.
6. What is the net viihie of a bill of books
09
amounting
to ^568.50 with 10 per cent. oH' for cash F.:/
e. What is the net value of a bill of goods amounting
to $4372 at 15% discount and 2^% off for cash ? ■ - - :
7. Goods are invoiced at $0500, less 8 per cent, and
6^ per cent. Find the cost.
8. Find the net amount of a bill of $930, discounts
being 33J, 20 and 2,^.
0. List price, $150. Discounts, § and ITJ.^^Find the -
cost price. -■ / ' *' . • . .
10. A dealer sold 2631 bushels of wheat at $1.13 a. i/
bushel Jes^a2i%. and 342 tons of hay at $17.50 a ton?!^
less 157^,' He allowed a further discount of 5% for cash.'
Find the net amount of the bill. ^ ' ' ^ - "
11. Montreal, April 11, 1896. — Edward Green,
Waterloo, bought of Thompson & Co., 36 pairs of boots at
$5.17; 216 pairs thick shoes at $1.37i; 135 pairs gaiters
at $1.38 ; 240 pairs buskins at $0.83 ; 134 pairs slippers at
$0.68 ; 87 pairs rubbers at $1.13. Discounts, 20 per cent
and 5 per cent. Write out the above invoice and show
net amount of the bill. - "
12. What is the difference on a bill of $200 between a
discount of 30% and discounts of 20% and 10°/ ?
XIX.
PRESENT WORTH.
The present worth of a debt is the sum which put at
interest is sufficient to discharge the debt when it
becomes due.
1. I have to pay $106 in a year from date. What
sum of money should I put at interest at 6 per cent, in
order to discharge the debt when it falls due ?
60
COMPOUND INTEREST.
2. I have the option of paying $208 a year hence, or
$200 now ; which is better, money being worth 4°/ ?
a A creditor agreed to allow discount at themte of
^ U for the immediate payment of a debt of $210 due in
lyear. How iimch Vvvuld the debtor need to pay ?
4. What is the present worth of $420 due 1 year
hence at 5 per cent. ? What is the discount allowed for
mimediate payment ? .' -
Find the present worth and true discount of :-^Jm
5. $420 due 3 years hence at 4 per cent. ^ ' ' - . ,-
6. .^1260 rliiP A v«ova 1,^,,.^ „^ o , -- ^y -^
7.
8.
9.
10.
^ xxiv^iiuiio au uj per cenc ^
$420 due 3 years hence at 4 per cent.
$1260 due 4 years hence at 3 per cent.
$170.50 due 3 yrs. 5 mos. hence at 4 per cent.
$1018 due 219 days hence at 3 per cent.
$187 due 292 days hence at 2\ per ceiiL
$322.35 due in 8 months at 3^ per ceffi*
XX.
v..
COMPOUND INTEREST.
^'X
6 Lf,0(-
y
Find the compound interest ^
1. For 2 years at 6% on $800 ; on $625. ^
2. For 2 years at 4% on $375 ; on $775i ' '.' /' 6 J >1 u
3. For 2 years at 31% on $675 ; on $720. ,;). . , ^^ -! ' ,
Fiml the amount ' j ' '
4. Of $240 in 2 years at 5°/^ compound interest ;j ^^t, L ;, I
6. Of $1000 in 3 years at 57^ compound interest. hXy^^
6. Fmd the compound interest on $100 for U years '^ ~
at 3 per cent, quarterly, /i^r /J ^"5 '^ . ■
7. What is the compound interest and amount of
$52.62 J for 3 years at 5 per cent. ?<?f -^ (f^/ ^ ^ .6;_2
8. Find the difference between the simple and com-
pound interest on $2000 for 2 years at OJ per cent,. 7 . f 7^
BAPID ARITHMETIC.
61
XXI.
RAPID ARITHMETIC.
P
$14.10
10.80
94.00
29.35
50.47
18.9D
A {Siglit).
A B O D B
53 33 $7.42 $5.86 $86.94
95 59 2.19 3.79 73.57
49 45 7.83 4.00 80.00
74 38 9.00 2,52 53.78
87 16 6.48 3.13 45.80
68 27 8.37 7.75 11.16
1. Add each number under A separately to each
number under B.
2. Find separately the difference between each num-
ber under A and each number under B.
3. Add each sum of money under C separately to
each sum under D.
4. Find separately the difference between each sum
of money under C and each sum under D.
6. Add each sum of money under E separately to
each sum under F.
6. Find separately the difference between each sum
of money under E and each sum under F.
7. Subtract sixes from 100, from 99, from 98 from 97
from 96, from 95, continually till the remainder is less
than 6.
8. Subtract sevens from 100, from 99, from 98, from
97, from 96, from 95, from 94, continually till the
remainder is less than 7.
62
RAPID ARITIIMKTIC.
Ji
m
II
A.
24
36
30
32
2S
16
15
25
42
48
B.
14
18
22
27
21
44
40
60
55
35
O.
72
66
64
70
63
56
96
64
81
40
D.
58
39
69
87
59
34
47
86
43
83
9. Subtract cif/hts from 100, from 99, from 98 from
97, from 96, from 95, from 94, from 93, continually till
the remainder is less than 8.
10. Subtract niiies from 100, from 99, from 98 from
97, from 96, from 95, from 94, from 93, from 92*, con-
tinually till the remainder is less than 9.
B (Siffht).
} 2S ll
' 21 4.
» 63 5(
• 59 34
1. Ikultiply each of tlie above numbers separately by
2> by 3, by 4, by 5, by 6, by 7, by 8, by 9.
2. Multiply each of the above numbers separately by
20, by 30, by 50, by 25, by 100, by 600, by 4000.
3. Find separately 17 , 27 . 77 8°/ 9°/ 10°/ 90° /
^^ /o' ^^^ /o 0* each of the above numbers.
4. Multiply each of the above numbers separately by
•5, by 425, by 1, by -001, by -2, by '8.
6. Find the cost of articles represented by the abov
numbers at the following prices :
$0.50 each. $0.05 each. $0.12J each.
.15 « $0.37*
).20 « S0.33J " $0.62J
).10 " $0.66f « $0.87J
6. Multiply 81-6, -086, each by 10, by 100, by 1000
7. Divide 97-8, -005, each by 10, by 100, by 1000
8. Multiply 1-6, 6-4, 8-4, 12, each by 20, by 40 bv
60, by 80. ^ ' ^ ^^> ^^y
O. Divide 1-6, 6-4, 8-4, -12, each by 20, by 40, by 50
by 80. '
tc
€t
U
8J each.
$0.16J
$0.75
$1.25
tt
€t
H
BAPID ARITHMETIC.
63
C (Sight).
DRILL EXERCISES TO SECURE RAriDITY AND ACCURACY
IN BUSINESS ARITHMETIC.
1. Read the followiug decimal fractions (a) as parts
of a dollar, in cents or dollars and cents, (/;) as rates per
cent., (c) as common fractions in lowest terms :—
31. 3125.
32. 8-575.
33. 6-775.
34. 4-925.
35. 1075.
36. 5-55.
37. 8-2.
38. 7-65.
39. 3-225.
40. 9-875.
1. -4. 11. -825. 21. -275.
2. -a 19. -525. 22. -15.
3. -6. 13. -375. 23. -1.
4. -3. 14. -975. 24. -35.
6. -9. 15. -675. 25. -475.
0. -7. 16. -025. 26. -125.
•7. '45. 17. -85. 27. -625.
8. -95. 18. -5. 28. -175.
9. -75. 19. -25. 29. -05.
10. -325. 20. -425. 30. -725.
2. Find the percentage in following (25 examples) :—
l^ase. Rate.
1. Sioo. («)57.
2. $50. (h) 47°
3. $2000. (,) 107.
4. $1200. (d) 2^/.
5. $250. (e) QyJ
3. Find tlie base in the following •
Perceutage. Rate.
1. $3. (a) 57^.
2. $15. (h) 47.
3. $0.50. (c) 10°7 .
4. $2.50. (d)2iy,
6. $10.50. (e) 1217.
64 RAPID ARITHMETIC.
4. Find the rate % in the following :—
Percentage.
Bi
ase.
1. $50.
2. $200.
3. $100.
4. $1000.
6. $2000.
(a) $10.
(h) $5.
(c) $15.
(d) $25. -
(e) $40.
5. Find selling price in following (30 examples) ;
Cost price.
1. $100.
2. $500.
3. $20.
4. $350.^
6. $10.
Rate 7o profit or loss.
(a) 57^ profit.
(6) 57^ loss.
(c) 107^ profit.
(d) 207, loss.
(c) 307, profit.
6. $120.
6. Find the profit or loss °/^ in the following :--
Cost price.
1. $100.
2. $200.
3. $400.
4. $000.
6. $800.
6. $1200.
Gain or loss.
(a) $20 gain.
(h) $20 loss.
(c) $40 gain.
(c^) $60 loss.
(e) $5 gain.
7. Find the cost price in the following : —
Selling price.
1. $120.
2. $150.
8. $300.
4. $750.
6. $600.
6. $3000.
Rate 7o profit or loss.
(a) 20 p.e. gain.
(h) 20 p.c. loss.
(c) 25 p.c. gain.
(d) 25 p.c. loss.
(e) 50 p.c. loss.
W'
RAriD ARITHMETIC.
fJ^
8. Find the simple interest on ((50 examples) ;
Principal
1. $100
2. $300
3. $500
4. $1100
5. $1200
6. $r)0
7. $150
8. $250
9. $1000
for
Time.
\a) 5 years at 4 per cent.
{h) 8 years at 4 per cent.
{c) 6 years at 3 per cent.
{d) 4 years at 2^- per cent.
{e) 2% years at 2 per cent.
if) H years at 2 per cent.
9.
10. $450 ^
Find the lime in the following (25 examples) :-
Principal. Rate.
\a) $100 at 1 per cent.
{h) $;]00 at 2 per cent.
{c) $400 at 3 per cent.
{d) $450 at 4 per cent.
\{e) .$400 at 2^ per cent.
Intci'est.
1. $45 "^
2. $54
3. $60
4. $90
5. $120
10. Find the rate in the following:
Principal.
\a) $100
(&) $500
(c) $200
{d) $250
l(t') $200
Interest.
1. $25 ^
2. $45
3. $30
4. $150
6. $135^
11. Find the principal in the following:
Time.
1 year.
2 years.
3 years.
8 years.
2i years.
Interest.
1. $7001
2. $450
3. $;]oo
4. $850
6. $250J
\
Rate. Time.
\a) 1 per cent. 1 year.
{h) 5 per cent. 2 years,
(c) 3 per cent. 4 years.
{d) 2h per cent. 6 years.
{e) IJ per cent. 2 years.
66
RAPID AiaillMETIC.
Add vertically and horizon tally, without copying down.w
8.
0.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
1
7003
5088
70G6
8G44
3716
0215
9284
7107
5006
7013
8015
7008
3728
6069
I
22
29. 90G7
30. 569
31. 3021
32. 705
33. 808
34. 906
35. 5002
36. 7006
37. 769
38. 606
39. 7021
40. 906
41. 6086
42. 509
2
8025
9067
5067
3815
9205
7063
8435
9219
80;2
9586
9080
7025
8004
7021
23
3706
109
2006
7006
9006
5060
7021
9117
9009
3967
1509
62
384
1055
3
9051
8007
2308
7016
5008
7046
3021
8069
8729
95G9
7219
6068
7216
6585
24
207
3709
9216
806
7219
3003
2016
707
9061
729
3069
501
15
7020
4
2107
3206
9063
8025
9206
3058
7021
9086
5721
3102
8607
2'»06
3106
8207
25
6064
7216
9608
3016
7213
9065
7213
906
7008
6068
7213
900
7906
612
5
1006
3003
7067
8206
3015
7068
5069
8725
9683
7025
8067
9213
3506
26
2001
786
2007
726
3015
900
7203
506
9603
729
1901
729
839
8879
6
7206
9025
8396
7215
9604
3726
9063
7158
3102
2002
7206
9608
3728
7
9020
7210
1856
1876
9215
3734
1000
2100
7200
6000
9989
7005
7683
7007 1559 9215
27
9002
2071
6068
7219
3068
7065
8219
2007
956
7029
606
7968
707
1906
28
6900
900
9000
9000
8888
777t
6660
6506
7766
9085
703
37
6921
fi9n
H
RAPID AUmiMETIC.
67
7
902G
7210
185G
187G
9215
37')-i
1009
2100
7200
6999
9989
7095
7683
9215
43
44
45
46
47
48
40
290G1
50216'
29113
39061
12345
96044
60.
»
70635
79613
7029
72096
67891
3726
51.
92186
80156
69031
59185
23456
96921
52.
59147
0 7007
79103
72096
78912
72156
53.
99081
30916
80217
3095
34567
9213
54.
79G98
50911
^ 9056
69002
89123
87215
55.
39091
72196
89215
7358
45678
9061
56.
87296
39167
90061
92015
91234
70123
57.
99896
90l>6
7213
8017
5G789
9686
58.
79684
907'.G
98175
29163
1237
500
59.
59607
9667
3007
7215
86041
72156
60.
79061
39286
90216
96003
88139
9 ^^ .i. x./ \J
36363
61.
59692
99081
72136
7215
71031
59081
62.
79683
-7296
9021
27568
6944
7216
63
64
65
66
67
68
69.
29137
90716
70140
40317
40211
20191
70.
59038
3824
92382
9856
70130
79386
71.
29537
96864
90368
47256
9035
59406
72.
90613
72196
59376
89666
79032
39601
73.
96928
39185
90213
37694
80965
89063
74.
57216
96072
7G384
59465
79632
79158
75.
90317
38067
96058
70315
1560
9091
76.
20313
47215
37213
96018
9G876
^•f \y tj ju
19090
77.
69681
90516
96474
86219
94032
70215
78.
72136
38296
58169
47206
5968
90217
79.
9063
39285
39467
96081
11411
5038
80.
70031
37216
29G06
47216
5917
4715
81.
2931
P* /% O /• rt
90213
70915
17129
86928
9624
C3^.
U"JO0C>
13729
80706
29615
37169
7968
r
68
RAPID ARITHMETIC.
Make out the foUowiiiL' bills :—
1. 5^ lbs. cheese at 9/.
3 1 lbs. clieese at 8/.
16 lbs. 12 oz. bacon at 8/.
14| lbs. ham at 11/.
9f lbs. lard at 7/.
8L doz. eggs at 14/.
3. 71 lbs. soap at 3|/.
5^ doz. lbs. soap ai 8J/.
5 bars do. (each 3 lbs.) at 4/.
18 doz. lbs. candles at 6|/.
13 J qts. oil at 6/ per gaL
3 J gross matches at 5/
per dozen boxes.
5. 52 yds. alpaca at 19/.
3 pieces merino (each 29|-
yds.) at 27/.
4 pieces poplin (each 156
yds.) at 54/.
14^ yds. lilac silk at $1.40.
11^- yds. black silk at 43i/.
3 1 yds. satin at $1.50.
Package, 42/.
7. 13 J yds. carpet at 54/.
18 yds. drugget at 25|/
5J yds. matting at 57/.
30 yds. binding at If/.
8| yds. oilcloth at 38/.
5 mats at 66/ each.
Less discount of 7J per
cent, for cash.
2. 3J lbs. tea at 40/.
7i lbs. tea at 46/.
21 lbs. sugar at SJ/.
3 J doz. lbs. sugar at 5 J/.
6 J lbs. coffee at 20/.
9 lbs. cocoa at 19/.
4. 3 1 yds. calico at 6/.
8f yds. calico at 8/. '
19^ yds. grey calico at 9/.
ISJ yds. flannel at 36/.
11 J yds. ticking at 24/.
5^ yds. linen at 28/.
3 1 yds. linen at 42/.
6. 13 lbs. 5 oz.,beef at 8/.
lljlbs. beef at 11/.
3 legs mutton (each 8
lbs. 8 oz.) at 91/. .
2 shoulders mutton (each
7 lbs. 5 oz.) at 8/.
10 lbs. 8 oz. veal at 10}/.
5 J lbs. pork at 7/.
8. 3 vols. Cowper at 60/ vol.
3 void. Longfellow at 42/.
1 set Waverley Novels (24
vols.) at $1.02 per vol.
13 quires foolscap at 8 J/.
3 J reams note at 4/ quire.
3250 envelopes at 6/ 100.
64 five-cent stamps, 54
two-cent do., 152 cent do.
RAPID ARITHMETIC.
69
9. 30 lbs. leaf tobacco at 84/. 1 0.
8 lbs. 3 J oz. Virginia
at 96/.
15 J lbs. Virginia at 90/.
13 boxes cigars (each 3J
lbs.) at $1.32 per lb.
9 boxes Havanas (each 4
lbs.) at $1.89 per lb.
57^ discount for cash.
28 lbs. cut nails at 9/.
13i lbs. cut nails at 10/
6 lianimers at 70/ each.
6 chisels at 21/ each.
13^ gross screws 5/ doz.
8^ gross screws 10/ doz.
1 doz. rakes at 15/ each.
3 spades at $1.08.
15 J lbs. white lead at 8/.
1.
2.
3.
4.
6.
6963519 X 8090
6978954x3906
6931768x8009
672976x5006
705968x6069
6. 7215698x5098
7. 99278x8837
8. 928417x8300
0. 6976x6976
10. 3884x3884
11. 9608x9608
12. 5327x5327
13. 8796x8796
14. 694x694x694
16. 765x765x765
16. 308x308x308
17. 8907x8907x8907
18. 6009x6009x6009
19. 9876x9876x9876
20. 967188x34562
21. 6990880x409006
22 2340600x607098
23. 2159063 -f 729
24. 926104513^217
25. 37l321617-r546
26. 70213169 -f- 947
27. 6120l793-r795
28. 713061311^864
29. 49031702^979
30. 47603136-^-847
31. 6956982-f861
32. 12345608 -f 987
33. 391760344-5968
34. 72041358-^9215
36. 20304054-4725
36. 43728514-6104
37. 192736653 -r 3856
38. 615274528 -f 7648
39. 706050494-8570
40. 4678179384734-2100
41. 3678179384294-36500
42. 2678179381154-1360000
43. 1,000,000,000,000,0004-81
111,11111.
70
MISCELLANEOUS EXAMPLES.
I
MISCELLANEOUS EXAMPLES.
A {Simple Mules).
1. Y'lM the sum of nil ih:-. numbers between 897
and 904.
2. The product of two numbers is 252 and the multi-
plier is 18 ; find tlie niultiplicund.
3. The sum of two numbers is 250 and their difference
is 50. Find the numljers.
4. The lei^s of two numbers is contained 14 times in
252 ; the^gre}>ter is^49 times the les8. Find the numbers.
6. What number multiplied by 789 gives 3771420 ?
6. Divide 900 into two Darts so that one may be 62
more than the other. -CCL^/
7. Express in words the following numbers :— 70070
707, 5706, 9011610, 3210, 10176, 40400.
8. Take thirty-seven millions thirty-five thousand six
hundred and eighteen from 110011007; and give the
result in words.
0. How many dozen are there in 126 score ?
1 0. Multiply half of 1162 by twice the third part of 402.
^ 11. The sum of 250 and 173 is multiplied by their
difference, and the product divided by 4j; what is the
quotient ?
12. If every page of a book contains 36 lines and each
line on an a\erage 11 words, how many pages will be
filled with 62172 words ?
13. I multiply a number by 36 an*" divide the result
by 12 and obtain 374181. What is the number ?
14. What number must be added to 32684 to make it
exactly divisible by 126 ?
16. What number muPt be subtracted from 461633 to
make it exactly divisible by 758 ?
MISCELI^NEOUS EXAMPLES.
71
B (Gmnmvyi Fractions),
1. Find the sum of J, J, J, | and J.
2. From(Aof|o,'5):ake(Vof|).
a. Multiply the sum of f and ^ by their difference.
4. By how much is H of 15 greater than 14^ x 1.^ ?
6. At $;]^ a dpy, what can a man earn in 25} days ?
6. The dividend i« 42^ quotient ^ ; find the divisor.
P J- .1 .' ^""^'^'^ ^ "^^^ ^^^ ^20^ md some sheep
tor ^.)2\ ; what change from a 8100 bill ?
8. How much longer is G feet than J of a foot ?
0. What must be added to (31-27 +4,V) to make 8| ?
1 0. How many times is (3i - 1 1) contahied in 6} x U ?
1 1. What must be subtracted from (7i-r6J) to leave A ?
12. By how nmch does 7i divided by 6^ exceed 6 A
divided by 71-? ^^
13. 16f is J of what mimber?
14. 18| is fV of 'vhat number ?
15. A of a ship cost $8;]60; what is the ship worth ?
16. I spend I of my money and have $18 left: what
had I at first ?
17. After walking 12 1 miles I have still |i of my
journey to travel. How long is my journey ?
18 When 24 lbs. have been taken f >m a r:hest of tea
It IS \\ full. What was the weight of tue tea ?
19. If I buy Ji of a ship and sell | of what I buy
what part o^ the ship shall I still own ?
20. Afte. spen.iing f of my money and losing i of the
remainder, I have $21 left. What had I originally ?
21. I pay I of a debt in silver, | in gold and the
remamder with 36 one-d.>lIar bills. What was my debt ?
22. A gets -jS. of an estate worth $4000, B ■§- of the
remainder, and C whaL is Ipft. TTnwp.,,pi, ^^.„ „^_._ ,,
- — u. — „ imtLii Qoeo uacii get f
72
MISCELLANEOUS EXAMPLES.
U I
II.
I
C (Decimals).
1. What is meant by the term "decimal fraction"?
2. Express in words •51:^2.
3. Kxproaa as common fractions -031, -0079, -001, 7103.
" J)ivide -031 by 10, and 1037 by 1000. '
From 1 iiiko -0031, nniltiply the remainder by -07.
I )i vide the sum of 825 and 4125 by their diilference.*
How many times can 125 be taken from 10 ?
What decimal represents the difference between
J and ^ ?
O. Add$-375 + $-0604 + S5-90G4-$30125.
4
6
6.
7.
8.
10. Add
11. From
12. From
13.
63 . 9-9
5-6 ''
5 J
•88
•57
•76
•36
take
•084
io-5*
take '^1.
5-2
Find tlie product of the two smallest decimals that
can be expressed by the finrures 0, 0, 9 and 3.
14. Divide 420 liundredtlis by 5 milliontlis and from
the quotient subtract 425 thousandths ; express the result
as a common fraction in lowest terms.
15. Cost of 6284 feet of lumber at .!;12.35 a thousand ?
16. Cost of 3684 lbs. of pork at $9.24 a hundred ?
17. One hundred and eight steps, each -581 feet hicrh
lead to the summit of a tower. What is its height ? ° '
18. The height of a dwarf is -1875 of that "of a giant
who is 8-88 ft. high. What is the dwarf's height ?
10. A person owns -675 of a business worth $47,500
What should he receive for -375 of his share ?
20. Simplify 111^ and give answer as a decimal.
MISCELLANEOUS EXAMPLES.
73
D (Compound Quantities).
1. Reduce 1 mi. 870 yds. 2 ft. to feet.
2. Reduce 4i:U 10020 seconds to years.
3. A boat race started at 2 hrs. 12 min. 11 sec. and
finislied at 2 hrs. 31 niin. 5J sec. ; how long did it last ?
4. Three gardeners rent 5^ ac. of ground; one has U
ac. and another 7216 sq. yds. How much has the third ?
6. If sound travels 1130 feet a second, how long does
It take to travel 226 miles ?
6. What is the total length in yards, feet and inches
ot 770 pieces of string each 29 inches long ?
7. From a plank measuring 19 ft. 6 in. there is cut
away 2 J of ^\ of the whole. What length remains ?
8. How many sixteenths of an inch in U yards?
O. Value of 7-125 of £5. 4s.
10. The cost of a cable message is 9d. a word; how
many words can be sent for £1. 3s. 3d. ?
11. Add together ^ of a bushel, f of a peck, i of 24
bushels, and -f of 7 bu. 3 pks. 4 qts.
12. Find the exact number of days between April 10
1890, and Aug. 25, 1891.
13. How many times round a garden 90 feet long 42
feet wide will make a walk of 3 miles ?
14. A ship sailing westward reached a point where its
chronometer at noon showed the time at Greenwich to be
6 hrs. 48 min. 28 sec. v.m. Find the longitude.
16. When it is noon at Montreal, long. 73° 25' West
what is the time in Paris, long. 2° 20' East ?
16. A circular track is 600 yards round; A runs twice
as fast as B; A and B start from the same place in
opposite directions, and they meet in 45 seconds. How
long would B take to run a mile at the same rate ?
H
MISCELLANEOUS EXAMPLES.
E {Prcportion).
1. If I walk 21 miles in 5 hours, how faj Jo I walk
in 2 hours? S" .-^
••' * ^
2. If 55 quires of paper are used in 18 days, how lono
will 33 quires last ? 0 :V^_ J > h
3. While a wheel 15 feet in circumference turns 400
times, how o^ten does a wheel 12 ft. in circumference turn ?'
4. If 75 lbs. of Lea last 8 persons for a year, for how
many days will 45 lbs. last them ? ,; , ^/ . ■ .
6. If 75 lbs. of tea last 8 persons for a year, how many
lbs. will be required for 146 days ? -^t ' ^
6. If 75 lbs. of tea last 8 persons for a year, how many
lbs. will be required for 12 persons ?
7. If 75 lbs. of tea last 8 persons for a year, for how
long will they last 20 persons ? ; ; ,
8. If 75, lbs. of tea last 8 persons for a year, for how
many persons will 600 lbs. suffice ? ^ V . • - ^ -
9. If 75 lbs. of tea last 8 persons for a year, how many
persons will they last for 292 days ?
1 0. If 25 men do a piece of work in 3^ hours, how
many can do the same work in 6f hours ? ' ,- y
11. A bankrupt pays 66| cents on the dpllar. His
assets are worth $452.50. What does he owe f^ > (^ >.i '
12. What does a bankrupt pay on the dollar, if his
creditors receive $850, and his debts are $3000 ? 7 .
13. A person travels 109 miles in 36 hrs. 20 min.; in
how many hours will he travel 50 miles ?
14. If the price of a score articles exceeds the price of .
a dozen by $2, what would be the price of 3 score and 10 ?'' '
16. Nineteen men perform a certain piece of y/ork in
76 days of 7 hours each; how many men would be
required to do it in 133 hours ? ,
I
x
A'
MISCELLANEOUS EXAMPLES.
F {Mensuration).
75
1. A garden fence is 63 yds. long and 9 ft. 4 in. high J
what will it cost to paint it on both sides at 11 cents a
sq. yard ?
2. How many boards 12 ft. 6 in. long by 9 in. wide
would be required for a room ll^ ft. by 10 ft. ?
3. The walls of a room 15 ft. long by 14 ft. 6 in. broad
and 8 ft. 6 in. high are to be painted, a window 5 ft. 6 in.
by 4 ft., and a fireplace 3 ft. 6 in. by 4 ft. being deducted
How many sq. yds. of surface are to be painted ?
4. What is the area of a piece of land in the form of
a rhomboid 200 ft. long, if the distance between the
parallel sides is 90 ft. ? ^; ^ ^
/ 6. Find area of blackboard surface in your room.
6. How many times will a wheel 3^ feet in diameter
turn m going 2| miles ?
7. In going a certain distance a wheel 4J feet in dia-
meter makes 1430 revolutions. What is the distance ?
8. If the equator is 25211-34 miles in circumference,
what IS the length of the diameter of the earth ?
0. The radius of a semicircular flower-bed is 20 feet *
find its area. '
10. Find the capacity of a round basket 20 in. in
diameter and 2^ in. deep.
11. Find the solidity of a prism whose base is 6 feet
square and height 15 feet.
^ 12. Of two pieces of land, the one a circle L8 rods in
diameter, the other a triangle whose base is 24 rods and
height 18 rods, which is the larger and how much ?
^ 13. What is the area of a triangular field whose base
V IS 325, yards and perpendicular height 160 yards. Express
m acres and square yards.
I
^^ MISCELLANEOUS EXAMPLES.
G {Metric System).
1. What is tbo price of a can of coffee containing 474-
Kg. at 2-20 francs the Kg. ? *
2. If the average weight of 5 packages is 4-625 kilos
and the weights of four of them are 3'675 kilos 8-675
Ivilos 2-25 kilos, and 7725 kilos; what is the weight of
the nrth ?
^ 3 If I walk 6-056 Km. in an hour, how far shall I go
in 6 hrs. 48 min. ? How many miles shall I go, allowing
a kilometre to be | of a mile ?
4, From 10-06 Km. take 354-406 m.
6. At 7/ a litre, what will a decalitre of milk cost ?
6. A druggist put up half a kilo of opium in boxes
containing 1| grams each. How many boxes did he need ?
7. How many grains of opium did each box contain ?
8 A litre of air weighs 1-3 grams; what will be the
weight of air in a room 3 m. long, 2 J m. wide and 2 m. high ?
9. Into how many lots of 3-75 a. may 8-40 Ha. be
divided ?
10. A vessel when empty weighs 1-02 Kg.; when full
of pure water it weighs 3-8 Kg. Find the capacity of the
vessel in litres.
11. A train which travels 56-25 kilometres an hour
take 3i hours between two stations What is the dis-
tance between them in metres ?
12. I can buy 526-2 kilos at $157.15 the kilo; what
would be the price per kilo, if I bought 1841-7 kilos for
the same monsy ?
1 3. A man cut 75-60 m. of wire into pieces each 25 mm
long, and sold them at 6)^ a doz. ; how much did he receive?
14. A cask weighs 227-5 Kg. more full than empty:
how many HI will 29 such casks hold ?
MISCELLANEOUS EXAMPLES.
77
H (Percentage).
1. In a shipwreck 45 people are lost out of 180;
what per cent, is saved ?
2. If a person spend 10% of his income in rent, what
has he left out of $460 per annum ?
3. In 1880 the population of a town was 129,181, and
in 1890 the population was 113,387. Find the decrease
per cent.
4. The population of a city increased from 401,321 to
460,428 ; find the rate per cent, of increase.
5. Find the prime cost of an article which, when sold
for $24, yielded a profit of 20%..>-
6. What per cent, of 2 ^ is 1^ ?
7. What is |% of $1728 ?
8. What is the difference between BhV of $800 and
6|% of $1050 ? .
0. A man received from a bankrupt $397.50, which
was 37|% of the sum due. What was his loss ?
^10. For what price per pair must shoes bo sold to gain
25^, if 15% is lost when they are sold at $1.27| per pair ?
11. A man owning 40% of a ship sold 25% oi his share
for $4500. What was the ship worth ?
^12. A sold two lots for $260 each, gaining 20% on one
and losing 20% on the other. Did he gain or lose on the
whole transaction, and how much ?
> 13. A buys a horse for $60 and sells it to B for $120,
who sells it for $200 ; how much per cent, did A gain'
more than B ?
14. Bought 60 barrels of flour at $8.50 a barrel. Half
'^ was sold at a loss of 10%, and the remainder at $9 a
barrel. Find the actual loss and the loss per cent.
78
MISCELLANEOUS EXAMPLES.
■' ' i'
fc_,-^-
I
amonnt to
I (Interest and Discount).
1. Interest on $290 for 11| years at 2J
2. Interest on $500 from May 15 to N(
3. At what rate per cent, will $50(
$5400 in 1. year 219 days It'^P'C,
<.Qn^ ^^ ""^^'"^ ''''^' P"" ''''^- ^^^^ ^^« «i°^Ple interest on
$300 amount to $36 in 4 years Ic^ <'
^ 6. In what time will the simple interest on $550
amount to $88 at 4%? ^ '^T^i -
^6. In what time will $6060 amount to $6696 30 at 3
per cent, per annum ? 3 "^
7. Whac principal will produce $50 in 4 years at 2 J
per cent, simple interest^* : v
8. What principal will amount to $377 in 4 years at
4/^ simple interest ?
.^^IZ ^""^ ""'"''^ ^ "^^^^^ '^^^^^ I ^e^t a house that
cost $o200, so as to receive 6% per amma fv/^
10. Find the net amount of a bill (A goods, the list
price of which is $435, discount 8% and 5% off for cash^, o,;,
11. On a bill of $025 what is the difference between a
discount of 30% and a discount of 26% and 5/ ? , i . ; f f-
Find the proceeds and discount on ° ° '•
12. A note for $700 drawn Nov. 13 at 90 days dis-
counted Jan. 1 at 7%. 6- ^^ ^ X L y 3- /> .
13. A note for $500 drawn July 9 at 90 days dis-
counted at date at 3|%. ^f^-. ^ ..i
14. A note for $400 drawn March 3 at 8 months, dis-
counted June 13 at 4 per cent. > ^"'3 "^. ^- Q '
^ 16. Find the amount at compound interest on $89 50
in 3 years at 5 per cent. / O I . h /
16. Find the difference between the simple and com-
pound interest on $5000 for 2 years at 4 per cent.^
TEST EXERCISES.
79
XXII.
TEST EXERCISES {Mental),
1. What is the largest number that can be formed by
the figures G, 0, 7, 4 ? . ^
2. How many apples must be cut up to give 300 boys
f of an ajiple each ?
3. Multiply 30 by 4, subtract 50, add 10, divide by 5
multiply by 7.
4. The remainder is 5, quotient 6, divisor 7. Find
dividend.
5. A woman bought 13 yards of goods at 30 cents a
yard. What change did she receive out of a $5 bill ?
6. I divide 25 oranges between 2 boys, giving one 7
more than the other. How many did each receive ?
7. What part of 10 miles is | of 8 miles ?
8. A horse costing $60 is sold for $75. What part of
the outlay is the gain ? What per cent. ?
0. If 8 pts. of berries cost 32^, what will a peck cost ?
10 A market woman having 6 doz. eggs broke 9 and
sold the remainder at 20^ a doz. What did she receive ?
1. How many days from April 24 to June 19 ?
2
3
What will a boy earn in 98 hrs. at 15/ an hr. ?
Prime factors of 210.
4. Express | of one-hundredth as a decimal.
6. Difference between 2^% and 3i% of $800.
« Value of ^ of a dollar.
Express f of a doIL:: a? a decimal of $2-J.
Interest on $40 !• i- 2} years at 57.
Divide 54-8 by 100. °
1 a Bought goods for $2| and sold for $3. Gain 7 ?
6
7
8
9
I" 1
80
TEST EXEIJCISES.
1. At 15ff a yard, liovv imicli can be bought for $3 ?
2. From a piece of cloth J and J of it have been cut,
Wliat part of it is left ?
3. J
our
its
How
much per gallon ?
4. What part of 100 is 121 ? wj^^^t p^^. ^^^^^ ^
6. By selling o. liat for $5.40 I gain 207 How
much do I gain ? ^°
6. I borrow $500 at 6% and pay it back at the end of
y months. What sum must I return ?
7. I bought 40 yds. of carpet at 75/ a yd After
iismg it 5 yrs. I sold it for $15. If the carpet was worth
a year to me while I used it, wliat did I gain or lose ?
a What is f of I of $10 ?
©. Bring li to a decimal.
10. Express 3 ounces as a fraction of 7 lbs.
1. Exchanged 11 tons of hay for 15 yds. of cloth at
and 4 yds. at $5. What is the hay worth a ton ?
2. How long will it take 11 men to do what 10 men
can do in 11 d.^ys?
3. In a certain school there are 20 boys and 4- as
many girls. Required the total number of pupils.
4. How many steps, each 2 feet long, will a child
take in walking 110 yards ?
6. A boy can pick 3500 stones off a summer fallow in
a day. At 20/ per m. how much will he earn in a week ?
6. A man bought some apples for 8S^' at the rate of 5
for 11/, and divided them among his 4 children. How
many did each child receive ?
7. 3 + J + 2 + J,
8. From 3-5 take 1-75.
0. What is -125 of a dollar ?
10. Interest on $44 for 3 years at 21%,
^'^
TEST EXERCISEa
81
for $3 ?
been cut.
1?
It.?
%. How-
he end of
i. After
^as worth
or lose ?
cloth at
>n?
10 men
nd I as
a child
allow in
I week ?
ate of 5
. How
I
by 128
Multiply IG by 12, add 8, divide by 400, multiply
2. At $16 acre, what will 2 ac. 40 rods of land cost ?
3. I buy 108 articles at i)^ for every 12, und pay for
them with a $2 bill. What change sliould I receive ?
4. The diil'ercnce in lbs. between i cwt. and J cwt.
6 Bought 4 bushels of nuts at 12J cents a peck. Gave
$2 bill. What change ?
6. Apples costing 2f' each are sold for 3/. Gain V ?
7. What is 4 of a dollar ?
8. Interest on $50 at 5% for 5 years.
9. I of a cent is what decimal of a dollar?
10. 5 oranges cost 7|/, what will 3 cost ?
1. If a plant doubles its number of IJossoms every
year, and lias two blossoms the lirst year, how many
blossoms will it have the liftli year ?
2. How many square tiles G inches on a side will be
required to make a hearth 4 ft. by 2 ft. ?
3. From | of a cask f of the cask is drawn off. If the
cask holds 48 gallons, how many gullons remain ?
4. Bought 3 quires 12 sheets of paper at 25/ a quire
VVhat change from a dollar ?
6. A quantity of sugar which weighed 900 lbs! lost
^/o m drying. What did it then weigh ?
6. If you buy a knife for 50/^ and sell it for GO/, what
per cent, of the cost do you gain ?
^ 7. A flight of stairs consists of 20* steps. Each step
IS 6 inches high and 12 inches broad. How many yards
of carpeting will be required to cover the stairs ?
8. What per cent, is 5 of 75 ?
0. Amount of $1000 for 10 years at 5y.
_ 10. From 8 times the half of 17 take 4x4x4.
i
82
TEST EXERCISES.
1. A.M 5, 18, 23, 7, 0, 14, 19, 3, S^k
.cot ^''f''^''^'^-'^^'^^-^-^^ and sold them at
ci cent each. Wliat was the gain on 10 gi'oss ?
3. If 20 men do a piece of work in 15 days, how lone,
will It take 12 men to do it ? ^
4. A man owns f of an estate and gives his son i of
his share ; what part of the estate has he then left ?
6. Whieh is greater and by how much, l yd. or ^ yd ?
6. How many lbs. sugar at 91/ ean be bought for $3.80 ?
8. Apples are 5 for 4f. How much per doz. ?
0. Cost of G| yds. ribbon at 6.1/ a yd. ?
1 0. How many scj. metres in tl^e walls of a room 12 m
long, 8 m. wide and 6 m. high ?
wm 7 ii rjr * ''^''' ^^ "''^^ '^■-■^ ''"^' "- ^"'="
2. J of a pole is in water. Tlie part al,ove water
measures 24 ft. What is the length of the pole ?
3 Three men did a piece of work. The first did -37
and the second -33 of it. What part did the tliird do ?
4. The product of the sum and diflerence of 18 and l"?
wil^; l" f ' ,T.' "^ " '""■' ^"' ^'^ '^'^y^ '"^ «»0> '^°>v muesli
Will it be for 17 days ?
6. A careless pupil wrote "7 instead of -07. What
was the amount of his error ?
7 A man sold something that cost him $240 at a loss
'^/o' ^V hat was the selling price ?
8. 4 cwt. of coal at $7.50 a ton. Change from $2
0. If 60 lbs. cost 84c, what will 65 lbs. cost ?
10. How many cubic decimetres in a rectangular stick
4 dm. square and 50 dm. long ?
of 25°
TEST EXERCISEa
83
1. A piece of work is done in 4 days of 12 hours each ;
how long will it take when the days are 8 hours ?
2. I pay away J my money and then J of what
remams, and have $3 left. How much had I at first ?
3. The four sides of a square room together measure
48 teet. Fnid its area in sq. yards.
4. Bouglit an article for $8 and sold it for $7. What
is the loss per cent. ?
6. A man sells GO sheep. This number is 66 f/ of
his flock. How many sheep in the liock ?
6. Cost of 2 gi-oss slate pencils at 3 for a cent ?
7. In -75 of a mile how many yards ?
8. What is $250 less 1% of $250 ?
9. On $oO I gain '5 of $10 in -5 of a year. Find ra^.o.
1 0. How many cubic metres in a cellar 20 m. lone/ 8
111. wide and 2J m. deep ? °'
1. Cost of 19 tons 1000 lbs. of coal at $6 a ton ?
2. How many minutes in a day ?
3. A farmer put 1200 bushels of wheat into 480 bags
of uniform size. How much did he put into each ba^ ?
4. An iron bar weighing 12 lbs. 8 oz. is made into 5
equal bolts worth 4/ a lb. What is each bolt worth ?
6. How much per dozen is 87i^ per pair ?
6. What must be added to J o"f 2f to make 1 ?
7. An assembly hall contains 20 rows of 15 seats each
and 30 rows of 5 seats each. How many will the hall seat ?
8. A woman is 42 years old, which is f of her hus-
band's age. How old is he ?
0. At 25/ a sq. foot what is the cost of a piece of
ground 20 feet front and 40 feet deep ?
10. A regiment of 800 men lost 8% of its number.
How many remained ?
u
84
TE«T EXEIiriSES.
1. How many tiine« will a wheel, 10 feet in circiun-
fereiiee, turn in going hulf-u-mile ?
2. }]y Helling goods at $7.20 I make a in-ofit of L'O per
cent. What did T give for tlxnu ?
3. What is that nuniher of which, if 8 be added, and
the sum divided hy 3, the quotient will be 12 ?
4. At 37?./ a yard, how many yards of lace can be
bought for So I ?
6. How many lioiins from noon of the 4th to midni<Tht
of the 7th July ?
6. If 20% be lost on a ton of hay sold for $19.20, what
was the cost of the hay ?
7. What will a mile of wire cost at a cent a foot ?
8. Two men chop 20 cords of wood in 4 days. How
many men can chop half the wood in half the time ?
0. Interest on $150 for 7 years at 4%.
10. A man lends $900 for 73 days° at 6%. Wbat
interest should be receive ?
I
1. 225 is 25 per cent, of a certain number. What is
the number ?
2. Sugar weighing 900. lbs. lost 10% in weight in
drying. What will it bring at 5/ a lb. ?
3. Cost of 250 lbs. of ice at $4.80 a ton ?
4. $25 less 4%.
6. $350 plus 3%.
6. What is ]^ short of 20?
7. Express 7 cwt. as a common fraction and as a
decimal of a ton.
8. What per cent, is 8 of 60 ? .
9. How many times is 15 contained in 6 ?
10. From J take f and express answer as a decimal
^W"
TEPT EXERCISES.
1. Ptoduce 6 pocks to frn« lion of 1 bushc
2. Express -^^ as a decinml.
8. Interest Sb"4, 7%, 1 year. Find principal.
4. Principal $200, amount 8400, 8%. Find tima
5. Multiply 3-5 by 12.
6. ou! § of $10 take i of ?^^
7. Interest is $3 at J ., .di at 3'/^ ? *
^. iV of 2 minutea
O. iVof2dayp
10. How uian) iours in 225 days ?
S5
1. 19 + 29 + 39 + 49 =
2. Express \ yard as th' "-action f f a rod.
3. How much is 20 times ^ of 10 cents ?
4. Bought an apple for If, sold for ly. Gain 7 ?
6. Take -75 from f . " '"
e. 2500 marbles at $1.60 a thou.-^ >nd.
r. Express -725 as a common fraction.
8. I acre is worth $120. What for ^ acre ?
9. From -07 take -007.
la Interest $50, rate 5%, 4 years. Find principal
1. Divide I of 1347 by A of 449.
2. What is 500 less 3% ? .
3. 2 gross pens at 9^^ a dozen.
4. At 22 cents a lb., how much for 2 oz. ?
5. How long will it take $300 to double itself at 5% ?
6. How Liany five-cent pieces in -25 of $8 ? ' °
7. How many inches in 3-75 yards ?
8. Amount of $400 for 4 years at 3|-%.
0. If I of a house cost $6000, what for the whole ?
10. Divide I of f by f.
"f
mm
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IMAGE EVALUATION
TEST TARGET (MT-3)
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23 WEST MAIN STREET
WEBSTER, N.Y. 14580
(716) 872-4503
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86
TEST PAPER&
xxni.
TEST PAPERS.
1. What number contains 3756 exactly 13|- times ?
2. Cost of 75^ doz. eggs at two for li cents.
J'^ 8. How many sleepers, each 3 ft. apart, would be
(required for a double line of rails 3| miles long ?
4. Cost of 11 yds. 2 ft. 6 in. of iron palisades at $3.75
a yard ?
6. If 35 workmen can do a piece of work in 18 days
how long would it take 210, working only half as quickly?
e. How many bricks, each 9 in. by 4| in., will pave 3
courtyards, each 81 feet square ?
B
1. If a man walks ^ miles in 2i hours, how far can
A he walk in 3^ hours ?
2. How much greater is the area of a lot 50 rods
square than of a lot containing 50 sq. rods ?
8. A farmer sold in a week 5*825 tons of hay. On
Monday he sold 1350 lbs. ; on Tuesday, i ton ; on Wed-
nesday, IJ tons; on Thursday, 1-415 tons; and on Friday,
1} tons. How much did he sell on Saturday ?
4. Express 2 ft. 7^ in. as the fraction of 100 yds
6. 1 A - (i of 4).
6. In a school numbering 200 the daily attendance is
160. What is the per cent, of attendance ? The number
absent is what per cent, of the number present ?
C
^ ^ 1. A train travels QJ miles in ten minutes; how far
"will it go in 1 hr. 45 niin. ?
TEST PAPEK3.
SI
2. Multiply tlie liulf of 7} dollars by 7.
3. Divide 3 times the half of 1108 by 5 times the
fourth part of 7 times 16.
_ 4. From $3-1475 take $310475 and reduce the
remainder to the decimal of 50 cents.
5. If a i)erson receiving $42 a week gets an advance of
15%, what will he then receive ?
1^ 6. Find the area of a triangle whose base is 9 fc 8 in.
and perpendicular height 5 ft. 3 in.
D
1. f of a week + f of a day + f of an hour.
2. What fraction of 25 lbs. is 3 lbs, 2 oz. ? What
per cent. ? What decimal ?
— , 3. If f of a yard of ribbon cost $J, what will be the
price of 5f yards ?
4. A man earns $2.75 a day. How much will he earn
in July, the first day of which is Thursday ?
6. Find | of 8 tons 16 cwt. 24| lbs.
6. -475 cwt. + -75 lb. + -125 oz.
1. What is the profit on the sale of 7 gross, 3 score
and 3i dozen newspapers a^t one cent each, if they are
bought at. 81- cents a dozen I'J 'J - .:.
2. In a town containing 11,500 inhabitants there are
22 deaths and 73 births per year in each thousand. Wliat
will be the increase in 20 years ?
- 3. A field of 7 ac. 80 rods is rented for $37.50. How
much is that for 19 ac. 120 rods ?
i,' 4. Simple interest of $720 from March 11 to July 9
at 7| per cent.
6. Take 2\ from the sum of 5f + 7 ^^ -|- 3«.
6. How many yds. of carpet a yard wide for a room
27 ft. long, 21 ft. 3 in. broad, if strips run across room?
m
I. ,
88
TEST rAJ'^KS.
1. Value cf i_^Ji of 21.
i X I-
9. Gained 12f /^ by selling eggs for f cent apiece.
What was the cost price per dozen ?
3. How many pieces, each measuring 2^ inches, can
be cut from 90 yards ?
u^. Kent of a house for 5 wks. at $260 a year?
6. Express fd. as the decimal of £1.
6. A square court whose side is 42 yds. is paved with
28,224 square tiles. Find the dimensions of each tile.
1. Cost of 700^ feet of boards at $22.50 a thousand.
2. Cost of -725 of a ton at $8 a cwt.
,/ 3. What is the profit per cent, on goods bought for
$11§ and sold for $14 ?
4. What is the weight in lbs. of the contents of a box
5 feet long, 4 feet broad and 3 feet deep, if 60 cubic
inches weigh 9 ounces ?
6. What is the total surface of a cube, the edge of
which measures 4i inches ?
6. What sum put at interest at 7^% will amount to
$2500 in 3i years ?
H
1. Bought 15 cwt. 22 lbs. of rice at $4.25 a cwt., and
6 cwt. 36 lbs. of barley at $5.60 a cwt. What will be
gained by selling the whole at G^f^ a lb. ?
2. A merchant sells cloth at $3.60 a yard, gaining
\207o. At what price must he sell to lose 15% ?
3. Kow much will it cost, including waste, to carpet a
room 18 ft. square with carpet | yd. wide, at $1.50 a yd. ?
4. Five cents a day is the interest on what sum at 7
per cent, per annum ?
TEST PAPERS.
89
6. The sum of two numbers is 187G. The greater ia
three times the less. Find the numbers.
6. From sixteen ten-tliousandths take 27 milHonths,
and multiply the difference by 20-5,
1. By how much does the difference between 5ff and
2f exceed the sum of |, ^^.^ and J ?
2. Add by decimals |, ^V, h '65, -375.
3. If -1-^ cwt. cost £7. 3s. what will -,«j. ton cost ?
jl 4. Simple interest on $9000 from March 8 to July 6
At 7^ per cent.
6. Cost of 18 ac. 136 sq. rods of land at $50 an acre ?
6. What is gained per cent, by buying coal by the
long ton (2240 lbs.) and selling it by the short ton at the
same price ?
J
1. J - -05 + J + -5 - -025 + } - J.
2. Eeduce 83 sq. rods to the fraction of 3 acres.
3. Cost of 3 tons 15 cwt. 10 lbs. at $12 a ton ? *
4. A garden 180 feet long by 150 feet wide is sur-
rounded by a tight board fence 6 ft. high. What will it
^ cost to paint the fence both sides at 12 cents per sq. yd ?
,j/ ^ 6. Interest on $125 from May 15, 1896, to December
/ > 20 of same year at 4 per cent.
6. If I buy at 60 cents a score, at how much a dozen "
must I sell to gain 40 per cent ?
K
1. How many loads of earth, each | of a cu. yd., must
be removed in making an excavation 21 feet long, 3 feet
wide and 3 feet deep ?
2. A man's interest on his money, invested at 67
gives him $90 a month. What is he worth ?
90
o/
TEST PAPERS.
3. Interest on $500 for 156 days at 7 per cent.
4. Add J, J, I, 1; subtract the sum from 2 and
multiply the result by f of j^.
5. A man earning $1.75 a day (10 hours) works on a
certam day from 1 p.m. to 4.30 P.M. What will he earn ?
6. How many yards of paper 30 in. wide will cover
the walls of a room 15 ft. long, 12 ft. wide. 8 ft. high?
L
1. Half the product of two numbers is -05 ; one of the
numbers is -0005. What is the other ?
^ 2. A farmer sold 24 doz. eggs at 22 J cents a doz., and
12 lbs. butter at 27i cents a lb. He was paid in tea at
• S/i cents a lb. How many lbs. of tea should he receive ?
3. Value of '965625 of a mile.
4. If gunpowder contains 75% of saltpetre, IO7 of
sulphur and 15% of charcoal, how many lbs. of each are
there in a ton of powder ?
6. The rent of a house is $330, which is 11 per cent
of its value. What is its value ?
6. What sum in 10 months at 417^ produces $3.96 ?
M
^ 1. A note for $730, dated August 3, payable in 3 mos.,
IS discounted Sep. 15 at 77,. Find the proceeds.
^2. In what time will $858 give $128.60 in interest at
6 per cent, per annum ?
^ 3. A man invests i- of his fortune in land, ^ in houses,
i m bank stocks, and loses the remainder, which was
$8000, in speculation. What was his fortune ?
4. Find the sum of the third, fourth, fifth, sixth and
seventh parts of 32760.
^ 6. Cost of 7i dozen books at 121- cents a copy?
[ 6. Find the volume of a square prism if each side of
its base is 4 ft. 6 in. and its height 20 ft.
TfiST PAPEKa
>
N
91
1. Cost of 912 lbs. of hay at $14.50 a toa
2. At what rate per cent, must I invest $600 that in
2J years it may amount to $705 ?
, 3. A man buys 1000 bushels of wheat for $1250.
XHe finds 15'/^ of it worthless. At how much a bushel
must he sell the remainder to gain 207^ on the cost ?
4. I have a sum of money. I deposit 80% of it in
the bank and afterwards withdraw 20% of the^deposit.
$5760 remain in the bank. How much had I ?
6. If a bird can fly 12 j miles in J hour, how far can
it fly in 5 J hours ?
6. What will be the cost of painting 8 circular pillars,
each 42 in. in circumference and 15 ft. high, at 20/ sq. yd.?
^ 1. What per cent, of f is J ?
2. If 200% of a number is f of 108, what is the
number ?
8. A note of $300, payable in 2 months, is dated Aug.
12 and discounted Sept. 1 at 6%. Find the proceeds.
4. Find the difference in time between two places
whose difference of longitude is 5'' 40'.
6. If I sell wood at $7.20 a cord and gain 20 per cent,
what did it cost me per cord ?
6. What is the area in acres of a triangular piece of
land whose base is 156 rods and height 63 rods ?
P
1. A careless pupil subtracted f instead of f Was
the answer too large or too small, and by how much ?
2. Cost of 76 bushels 2 pecks 1 gallon of clover seed
at $2.40 a bushel
3. How much must a man's salary be in order that 17
per cent, of it may be $204 ?
! r
92
TEST PAPERS.
4. Interest on $7300 from March 6 to August 3 at 7
per cent.
_ 6. In what time will 8525 give $257.25 simple
mterest at 7 per cent. ?
' 6. Find tlie cubic content of a round column of marble
, wliose diameter is 16 inches and height 12 feet
Q
' 1. Divide ^ of 2 1 by f of 1-4.
2. Heduce 1-047 of 2 weeks 5 hours to minutes and
the decimal of a minute.
^ 3. If sound travels at the rate of 1125 feet a second
m how many seconds after the flash would you hear the
report of a gun fired at a distance of 1-375 mile ?
4. Find (by practice) the cost of warming a building
for 11 dys. 17 hrs. 28 min., if the cost is $4.50 per day.
^ 6. Find the compound interest on $4500 for 2 years
p 4 per cent.
6. Find the circumference and area of a circle whose
radius is 2 ft. 4 in.
R
^1. From a vessel f full 22 gallons are drawn, and it
IS then J full. How much does the vessel hold I
2. Goods are sold for $7| at a loss of 8 per cent. Find
Uheir original cost.
^ 3. Find the number of bricks, 9 in. long, 6 in. wide 4
m,4eep, required for wall 18 ft. long, 1 ft. wide, 6 ft. high.
^ 4. What is the present worth of $1056, due 8 years
Iience, at 47^ per annum simple interest ?
6. Take J of -037 from the product of 2-307 and 60-3.
6. :Bought oysters at $10 a thousand and sold them*
cents a dozen. What is the gain per cent. ?
EEVIEW EXERCISBa.
93
REVIEW EXERCISES.
1. How may two fractions be added or subtracted
when the numerator of both is 1 ?
2. How multiply a fraction by an integer? (two ways).
8. How divide a fraction by an integer ? (two ways).'
4. What are complex fractions ?
6. How do weights and measures in the Metric
system differ from those in the English system ?
e. What is the base of the Metric system ?
7. How are names of higher denominations formed ?
8. How are names of lower denominations formed ?
O. What is the standard unit of length ? Of capacity?
Of weight ? t^ J
10. Which units are most used in measuring length?
Surface? Volume? ^ ^
11. Which units are most used in measures of capacity ?
In weight ? ^
12. For what is the are used ? The stere ?
18. How are compound quantities, expressed in the
Metric system, added, nmltiplied, subtracted and divided ?
14. What is mensuration ?
15. What is a straight line? A perpendicular line?'
Parallel lines ?
iO. What is an angle? A right angle? An obtuse
angle ? An acute angle ?
17. What is a parallelogram ? Draw, name and describe
four kinds of parallelograms.
18. What difference between a square and a rhombus ?
19. What is the difference between a rectangle and a
rhomboid ?
20. What is a triangle ? A right-angled triangle ? An
equilateral triangle ? An isosceles triangle ?
ir
94
REVIEW EXERCISES.
21 Show by diagram how to find the area of a
pcarallelogram.
22. Show by diagram how to find the area of a triangle.
23. What isa circle ? The circumference ? Diameter ?
Ivadius ?
24. How find circumference when diameter is given?
26. How find radius when circumference is given ?
26. What is a cube ? A prism ? A cylinder ?
27. Wliat is a triangular prism ? A square prism ?
28. How find the solid content of a prism or cylinder ?
29. How find the upright surface of a cylinder ? The
total surface of a prism ?
SO. What does per cent, mean ? How is it expressed ?
31. How change a common fraction to per cent ? A
decimal fraction ?
82. In questions on percentage what is the base ? The
rate per cent. ? The percentage ? The amount ? The
difference ?
33. How find percentage when base and rate are given?
34. How find the rate from base and percentage ?
35. What are profit and loss ?
36. What is interest ? Principal ? Rate ? Amount ?
37. What is the difference between simple interest and
compound interest ?
38. What is discount ? True discount ? Bank dis-
count ? Commercial discount ?
39. What is a promissory note ? The face of a note ?
The proceeds ?
40. When is a note negotiable ? When does it mature?
How find the discount of a note ?
41. For what is circular measure used ?
42. What is latitude ? Longitude ?
TABLES.
96
WEIGHTS AND MBASURBS TABLES.
Time.
60 seconds (8ec.) = l minute (min.)
00 minutes =lhour(iir.)
iMliour* =ldjiy(ay.)
7 (lays =lweek(wk.)
3(55 (lays « 1 common year (yr.)
100 years =1 century (C.)
Capacity.
2 pints (pt.) = 1 quart (qt.)
4 quarts = 1 gallon (gal.)
2 pints (pt.)
S ((uarts
i pecks
1 quart (qt.)
1 peck (pk. )
1 bushel (bu. )
1 pint (water) weighs IJ lbs.
1 gallon contains 277 cubic inches.
Wkight.
16 ounces (oz.) = 1 pound (lb.)
100pounds= 1 hundredweight(cwt.)
20 cwt. or 2000 lbs. = 1 ton.
2240 lbs. s 1 long ton.
English Money.
4 farthings a 1 penny (d.)
12 pence s 1 shilling (s.)
20 shillings = 1 pound (£.)
Surface.
144 square inches ss
1 square foot (sq. ft.)
9 square feet = 1 square yard.
30| 8(iuaro yards = 1 square rod.
100 sijuare rods or ,
4840 square yards =" * ^^^ i^-)
640 acres = 1 square mile.
Volume.
1728 cubic inches = 1 cubic foot.
27 cubic feet = l cubic yard.
16 cubic feet := 1 cord foot.
8 cord ft. or 128 cubic ft. = 1 cord.
Miscellaneous.
12 units = 1 dozen.
12 dozen = l gross.
20 units = 1 score.
24 sheets = l quire.
20 quires = 1 ream.
4 inches = l hand.
6 feet = 1 fathom.
Length.
12 inches (i::.) = 1 foot (ft.)
3 feet = 1 yard (yd.)
5i yards = lrod(rd.)
320rods, 1760 yards , ., / • v
or 6280 feet =1 mile (mi.)
Troy Weight.
24 grains = 1 pennyweight (dwt.)
20 dwt. = 1 ounce.
12 ounces = 1 pound.
Circular Measure.
60 seconds (") = 1 minute (').
60 minutes = 1 degree (•).
360 degrees = 1 circumference.
69J miles = l degree.
96
TABLES.
Money.
lOOcentiinea m lfrano(fr.)
METRIC SYSTEM.
Capacity.
10 mllliHtre8(inl.) = i centilitre (ol.|
10 centilitres = 1 decilitre (Ul.)
10 decilitres = 1 litre (1.)
10 litres a 1 decalitre (Dl.)
10 decalitres = 1 hectolitre (HI.)
Length.
10 millimetres (mm. )=
1 centimetre (cm.) Weight
10 centimetres = 1 decimetre (dm. ) 10 milligrams (mu ) L
10 decmietres =1 metre (m.) i i ♦.
10 metres « 1 decametre /nm i in xs I centigram (eg.)
in A . uecametre (Um.) 10 centigrams = 1 decicram (da \
10 hectograms =1 kilogram (Kg.)
1000 kilograms make a metric ton.
Surface Measure.
100 square millimetres = i square centimetre (sq. cm.)
OOaquarecenWtres = 1 square decimetre (sc. dm.)
100 square decimetres = 1 square metre (sq. m.)
Land Measure.
100centiares(ca.)=l are(a.) 100ares = l hectare(Ha.)
A centiave is the same in size as a sq. metre.
Solid Measure.
im cubic millimetres = i cubic centimetre (cu. cm.)
000 cubic cenimetres = 1 cubic decimetre (cu. dm.)
1000 cubic decimetres = 1 cubic metre (cu. m.)
In measuring wood the cubic metre is called a Stere.
Equivalents.
1 metre = 39-37 inches.
1 kilometre = -6214 mile.
8 kilometres = 5 miles (nearly.)
1 sq. metre = M96 sq, yards.
1 hectare = 2 471 acres.
1 litre = 1-76 pints.
1 hectolitre = 22 01 gal
Igram = 15 -432 grains,
1 kilo « 2-2046 lbs.
1 metric ton = 1-1023 tons.
Prefixes.
Deca means 10.
Hecto
Kilo
Myria
Deci
Centi
MilU
100.
1,000.
10,000.
^•
)ntnitre(oI.|
litre (dl.)
(1.)
litre (Dl.)
alitre (HI.)
igram (eg.)
•am (dg.)
(g.)
[•am (Dg.)
fram (Hg.)
ram (Kg.)
netrio ton.
[. cm.)
dm.)
H».)
!m.)
1.)
0.
00.
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